## Opportunities ahead

Many students who take up higher studies in physics are often unaware of the various opportunities that await them. Even if they do, they find it difficult to surmount such barriers as national level competitions. Many a times it is their lack of basic undestanding of the subject, and in other cases their lack of prepartion that prevent them from scoring well in such exams. In order to soar high, bulding a sound knowledge of the basics is advisable.

Discussed below are several tangible opportunities achievable with a single devoted preparation for a masters degree student in physics, and in certain cases for bright bachelors degree students, as well. Even though there are a wide variety of options for success before a physics graduate who has the twin potential of mathematical reasoning ability and applied practical skills, we will focuss on a few exclusive options for physicists.

Being competitive in the job market means good understanding of the subject as well as thorough prepartion for specific examinations. We will discuss a few exams that test your competence and further pave way for a good career in the subject through research and development. If you are looking for employment right away after graduation, every employer will test your abilities in the following areas:

Verbal Abilities Quantitative Aptitude Qualitative Aptitude General Awareness To measure your ablities in these areas, various examinations, written and oral, will be designed. They invariably have the following structure:

– Reading

– Comprehension

– Analysis

– Writing

– Speaking (Personal Inverview).

Physics postgraduates can pursue their career in various government owned Scientific Research and Development Organizations such as Defense Research and Development Organization (DRDO), Physical Research Laboratory Ahmedabad, Nuclear Science Centre New Delhi, Saha Institute of Nuclear Physics Kolkata, Bhabha Atomic Research Centre (BARC) and Indian Space Research Organization (ISRO). Several other government organizations are also offering various jobs for these graduates. Some of those organizations:

Oil and Natural Gas Corporation (ONGC), Bharat Heavy Electricals Limited (BHEL), National Thermal Power Corporation (NTPC). We will discuss a few competitive exams that will launch your professional career in physics, either in academia or in research. If you can reach the level of competency to qualify any one of these, others in the list are also within your reach.

## The JEST Exam

Applicants seeking admission for a Ph.D / Integrated Ph.D Programme in Physics or Theoretical Computer Science or Neuroscience in one of the Participating Institutes may appear for the Joint Entrance Screening Test (JEST). Participating Institutes have their own eligibility criteria. Applicants who are expected to complete their final examinations by August of each year are also eligible to appear for the JEST exam of that year. Basic requirement is M.Sc. in Physics or related disciplines. However, talented final year B.Sc. and first year M.Sc. in Physics / Electronics / Astronomy / Applied Mathematics students are also eligible to apply for select courses at select places. More details can be obtained from the website www.jest.org.in that offers the application form, exam schedule, syllabus and previous question papers.

## The GATE Exam

The Indian Institute of Science (IISc) and seven Indian Institutes of Technology (IITs at Bombay, Delhi, Guwahati, Kanpur, Kharagpur, Madras and Roorkee) jointly administer the conduct of GATE. The operations related to GATE in each of the 8 zones are managed by a zonal GATE Office at the IITs or IISc. A valid GATE score is essential for obtaining financial assistance during Master’s programs and direct Doctoral programs in Engineering/Technology/Architecture, and Doctoral programs in relevant branches of Science in Institutes supported by the MHRD or other Government agencies. If admission is secured to any such institution following the MHRD guidelines, candidates can avail scholarship/assistance for their Masters or PhD study.

Several public sector undertakings (PSUs) have, in the past, used GATE scores for screening for providing a salaried employment. A select few such organizations are: Bhabha Atomic Research Centre, Bharat Heavy Electricals Limited, Indian Oil Corporation Limited, National Thermal Power Corporation, Power Grid India, etc. Also, various institutions abroad such as universities in Singapore give preference to GATE qualified students for admission into their Masters or Doctoral studies.

## The DRDO Scientist Entry Test (SET)

DRDO SET, whenever required, is conducted in the month of September, depending on the requirements, in order to provide equal opportunity to all students from different educational institutions in view of the increasingly wide variation in the marking pattern of different educational institutions in the country. DRDO SET exam is of three hours duration consisting of two sections viz. Section ‘A’ of 100 questions to test the candidate’s knowledge in the subject of Post Graduation and Section ‘B’ of 50 questions to the candidate’s ability in analytical and qualitative skills, current affairs and general awareness to test the aptitude and scientific knowledge required for Applied Research & Development. DRDO SET exam is conducted only for those subjects where vacancies are sizable in number. Details of eligible candidates, examination schedule, result of the exam, schedule of interviews and list of selected candidates are made available from time to time on their website (www.rac.gov.in)

In cases, where very few vacancies are available, no SET exam is conducted and the individuals after shortlisting are directly called for the interview. The advertisement generally appears during the month of April / May every year.

## Bhabha Atomic Research Centre (BARC)

BARC offers some of the best opportunities for physicists. Direct recruitments are usually limited and reserved for PhD holders. However, they run an excellent training school offering two different schemes as follows:

- One year Orientation Course for Engineering Graduates and Science post-Graduates (OCES). The program will be conducted at BARC Training Schools situated at Mumbai, Kalpakkam, Indore and Hyderabad. A Trainee Scientific Officer (TSO) who scores a minimum of 50% aggregate marks on completion of the training program is declared to have passed the course successfully. Successful TSOs will be posted as Scientific Officers in one of the eleven DAE units.

Appointment in DAE units shall be as a ‘Group A’ Gazetted Officer of the Government of India except in NPCIL, UCIL AND BHAVINI which are governed by the service rules of Corporations. Allocation of a successful OCES TSO to a DAE unit is done based on performance in the OCES program. Apart from the DAE units listed above, DAE reserves the right to place a small number of TSOs to any other unit under the Atomic Energy Commission (AEC) or the Atomic Energy Regulatory Board (AERB).

Performance above a specified threshold in course work at the Training School will entitle TSOs to a Post-Graduate Diploma or could earn them credits towards M.Tech/ M.Phil/ PhD Programs of the Homi Bhabha National Institute (HBNI), a Deemed to be University.

- Two-year DAE Graduate Fellowship Scheme for Engineering Graduates and Physics Post-Graduates (DGFS). Under this scheme, Engineering Graduates and Physics Post-Graduates who are selected for the BARC Training School program and who also have secured admission for M.Tech/ M.ChemEngg in select institutes and specializations are paid stipend and tuition fee to pursue a M.Tech/ M.ChemEngg degree while retaining their employment in DAE. After successful completion of one-year course work at the institute, fellows undertake project work, which is assigned by DAE and supervised jointly by a DAE and an institute guide. On successful completion of M.Tech/ M.ChemEngg, they are posted as Scientific Officers in DAE. On joining, they are required to first undertake a four-month Orientation Course (OCDF) at the BARC Training School, Mumbai. The DGFS fellows are enrolled and posted in one of the following units of DAE: BARC Mumbai, IGCAR Kalpakkam and RRCAT Indore.

Allocation of a DGFS fellow to a DAE unit is done at the beginning of the M.Tech/ M.ChemEngg program based on Selection Interview performance. Selected candidates are required to execute an agreement and a Personal Indemnity Bond to serve DAE for at least three years after completion of training.

Selection to OCES/DGFS is a two-step process: Screening to short-list candidates followed by Selection Interview of the short-listed candidates.

1) Screening for the Science disciplines is based on two alternative methods:

(a) On the basis of GATE Score: Candidates can apply on the basis of a valid GATE score (last two years). GATE cutoff score for short-listing candidates for Interview will be declared BARC in their website (http://www.barconlineexam.in).

(b) On the basis of Online Exam: Online Exam will be conducted during a selected period (second half of March for the 2014 exam). All candidates applying on the basis of GATE score can maximize their chances of being screened into the Selection Interview by applying additionally on the basis of the Online Exam, which will be held before the cut-off GATE scores are known. No Travel Allowance is paid for appearing in the Online Exam.

(c) On the basis of Interview: Candidates completed their degree in UNIVERSITY OF MUMBAI-DEPARTMENT OF ATOMIC ENERGY (CENTRE OF EXCELLENCE IN BASIC SCIENCES) or in NATIONAL INSTITUTE OF SCIENCE EDUCATION AND RESEARCH, BHUBANESHWAR are screened through interview only.

2) Selection Interviews of shortlisted candidates in disciplines other than Geology & Geophysics will be conducted in BARC Training School, Mumbai. Candidates are suggested to visit this website regularly for updates regarding this. Final Selection is solely on the basis of performance in Selection Interview subject to medical fitness.

## The Oil and Natural Gas Corporation (ONGC)

Oil and Natural Gas Corporation (ONGC) is a Maharatna company. Almost every year it recruits people from different backgrounds. Since ONGC is involved in the exploration and production of hydrocarbons it recruits students with physics background for jobs that will be interdisciplinary in nature, along with Geophysics and Geology. One of the best jobs on offer is ONGC is Class-I executive (E-1) for which there were are four categoriesapplicable to physics postgraduates, namely, E&T, Geophysics (Surface and Wells), and Reservoir. The Company offers one of the best compensation packages in cost to company (CTC) terms in the country with opportunity of merit-oriented advancement in a professionally managed organization focused on growth.

ONGC doesnot have a fixed schedule about the recruitment and Graduates Trainees exam like BARC, etc. The 2010 exam had two parts: General awareness and subject. An all India written test was conducted in 8 cities across the courntry, the nearest to Kerala being Chennai. The questions are objective in nature and there was no negative marking. In addition to this there were two descriptive questions in the general awarness category and two descriptive questions from the chosen subject.

## The Indian Oil Corporation (IOC)

Indian Oil Corporation is a Navaratna public sector company and is the largest commerical enterprise in India. If you can get at least three years industrial experience, the IOC occassionally calls for the post of Assistant Officers. Postgraduates in Physics, Chemistry or Mathematics can apply online for this post if they have experience in areas like processing, manufacturing, logistics, sales & distribution, services etc. However, experience in teaching, research and internship during or before postgraduation will not be counted as industrial experience. Applicants will be shortlisted on the basis of their GATE score for further selection process. The last application was called for in September 2012 and GATE 2013 score was used for shortlisting. Watchout for oncoming advertisements if you have a valid GATE score or have some plans to take the GATE exam soon. Age limit for this post is 30 and restrictions will be relaxed for SC/ST and OBC candidates based on the Presidential directive.

## The CSIR-UGC NET Exam for JRF and LS

The CSIR-UGC NET Exam for Junior Research Fellowship and Eligibility for Lectureship has become the norm for all aspiring postgraduate students of science in India to lead a successful career in research or academia. The exam has a Single Paper Test having Multiple Choice Questions (MCQs) with three different parts. It is therefore important to practice the art of scoring in such exams and the only way to succeed is to get a good grasp of the fundamentals of the subject.

### Applying for NET

The NET is held twice every year: in June/July and December. Keep an eye on the CSIR website (http://csirhrdg.res.in) which will tell you about all that you need to apply for the test. Before filling in the form, make it a point to have all the details with you (especially the subject code and centre code) since you won’t be able to change anything later on.

### Writing the Exam

The physical sciences exam will be held in the morning session and will be of 3 hours duration. The pattern for the Single Paper MCQ test shall be as given below:-

The MCQ test paper of each subject shall carry a maximum of 200 marks. The exam shall be for duration of three hours. The question paper shall be divided in three parts. Part ‘A’ shall be common to all subjects including Engineering Sciences. This part shall carry 20 questions pertaining to General aptitude with emphasis on logical reasoning graphical analysis, analytical and numerical ability, quantitative comparisons, series formation, puzzles etc. The candidates shall be required to answer any 15 questions. Each question shall be of two marks. The total marks allocated to this section shall be 30 out of 200.

Part ‘B’ Part ‘B’ shall contain subject-related conventional MCQs. The

total marks allocated to this section shall be 70 out of 200. The maximum number of questions to be attempted shall be in the range of 20-35.

Part ‘C’Part ‘C’ shall contain higher value questions that may test the candidate’s knowledge of scientific concepts and/or application of the scientific concepts. The questions shall be of analytical nature where a candidate is expected to apply the scientific knowledge to arrive at the solution to the given scientific problem. The total marks allocated to this section shall be 100 out of 200.

### Important Points to Note:

In all the subject areas of the NET the actual number of questions asked and to be attempted in each section may vary from exam to exam. There will be negative marking @25% for each wrong answer. To enable the candidates to go through the questions, thequestion paper booklet shall be distributed 15 minutes before the scheduled time of the exam. The answer sheet (OMR sheet)shall be distributed at the scheduled time of the exam.

### General Strategy

Considering the new pattern, we find that the key part of the exam is the last one. Here we have 50% of the total marks allotted and the questions will be from advanced physics topics. The next priority should be given to Part ‘B’ that has 70 marks. First attempt the questions you are absolutely clear and then attempt the remaining questions. There is negative marking and it takes practice and patience to answer this paper promptly so that you should avoid questions which you cannot score. If you have time, recheck your answersand try to get the maximum out of section ‘A’. To summarise:

Section C carries 50% weight with 5 marks for each question.

Section B carries 35% weight with 3 - 3.5 marks for each question.

General aptitude section can be tackled with a little bit of practice with similar questions from public exams.

### How to Avoid a Disaster?

The usual saying is, “when the going gets tough, only the tough get going.” So cover the difficult, yet important, portions of the subject to score a maximum. Candidates with good preparation survive in all situations and objective type questions demand good practice (unless, of course, you are a genius)! One thing you will notice among all those who qualify the test in one sitting is that they all show a kind of passion towards the subject and that will surely drive their entire career.

Though we cannot say anything about the cut off marks, experience tells that one has to score well in all parts of the exam to get a JRF. Some may have a tendency to give it up feeling dejected about the first part of the exam. Be cool in your approach to the exam and never give up during the examination by doing things like answering all the multiple choice questions randomly based on luck or feeling dejected of your performance. There is plenty of time to prepare and perform well.

### Why Negative Marking?

Negative marking is incorporated in any objective type examination to nullify the effect of gambling. If you look at it statistically, the maximum probable score one can get is 25% out of100 having four choices each. Remember, this is the maximum and sometimes there is a remote probability that you score a cent percentage. Rather, experience may tell you that you get relatively low score when you leave things to chance alone. Negative marking with one-fourth of the marks given to a correct answer tries to reduce the marks by chance.In examinations with objective type multiple choice questions (MCQs), there is a tendency called the ‘Red Wire Syndrome’ which means that one may answer all questions whether he or she knows the correct answer or not. If we can classify the questions into three categories: 1) Easy, 2) Fifty – Fifty, and 3) Extremely Lucky, indicating one knows the correct answer, possible but some doubt still prevails, and almost impossible, respectively. The ‘red wire syndrome’ is the tendency to answer all the questions, which is disastrous, just like a child who touches a ‘red hot wire’ seeing it as something beautiful! Be careful as the section C has 5 marks per question and a wrong answer would award you -1.25 in return!

The key to success lies in answering all the ‘easy’ ones, and leaving out the ‘extremely lucky’ type. It is imperative to learn the art of intelligent guessing to answer the type 2. There is no magic key to do so. This evidently comes from one’s experience and basic knowledge of the subject. So never ever find it insulting to go back to your basics (at least refer to some of the basic books in the list below). Also never forget to practice well using previous question papers of GATE, UPSC Civil Services, JEST, GRE (Physics), IIT JAM etc., so that you are prepared!

## Syllabus Based Strategy

### Part A (15 x 2 = 30 Marks)

This part shall carry 20 questions pertaining to general aptitude with emphasis on logical reasoning, graphical analysis, analytical and numerical ability, quantitative comparisons, series formation, puzzles etc.

If you go by the model question paper (never take it as it is), we can notice that it needs good practice if you are not familiar with such questions. A science student should not find them confusing (even if you do, there are choices).Refer to previous question papers of the Paper I of UGC NET (Arts & Humanities stream) examinations. Logical reasoning and numerical ability questions demand familiarity, clear concepts and practice to answer them. Refer to magazines and text books on the topic used by those who prepare for Bank PO, UPSC exam etc. There is no harm in taking some special assistance, if needed.

Let us set the target for this session as 12 correct answers out of 20 questions (i.e. 80% score). However, scoring 15/15 would add positively to your chances and that is not an impossible task!

### Physics Core (Part B & C)

Before you proceed to master the syllabus and art of scoring in the core physics area, take a break and think about your basic physics understanding. If it is not good enough, it is always recommended that you lay the foundation first and build further only on a solid ground. Some books and links are given below, but remember: “Working out your problems is the only key to success.” Given that the entire test is objective, good fundamentals and a problem solving strategy can easily get you a JRF!

### Recommendations for General Reading:

- NCERT Books on Physics – Go down to whichever level you want to and read up to class XII. Never a waste of time! Don’t worry about the costs: go to www.ncert.nic.in and download them as you wish!
- Principles of Physics - Raymond A. Serway & John W. Jewett: This best-selling, calculus-based text by award winning teachers is recognized for its carefully crafted, logical presentation of the basic concepts and principles of physics.
- Fundamentals of Physics – Resnick, Halliday and Walker: excellent introduction without much calculus. Lots of problems and review questions. Read the book throughout and workout as many basic problems as possible.
- Berkeley Physics Course, Vol. 1 – 5 (Tata McGraw-Hill): A very good bridge to cross from school level physics to the graduate level. They would give the necessary background for all our advanced studies and all the books are written by masters of the subject.
- Calculus and Analytical Geometry – Thomas and Finney (Pearson) {for those who want some basic math}.
- Concepts of Modern Physics – Arthur Beiser (Tata McGraw-Hill): Your pocket book to success in modern physics. Master this book and you are guaranteed of success!
- “HOW to BECOME a GOOD THEORETICAL PHYSICIST” by Gerard ‘t Hooft - A must read by the Nobel Laureate: http://www.phys.uu.nl/~thooft/theorist.html. This site contains a lot of free lecture notes and resources on several topics.
- Feynmann Lectures on Physics (3 volumes): highly recommended texts compiled from the undergraduate lecture course given by Feynman at Caltech.

Part B (20 x 3.5 = 70 Marks)

## Syllabus

### Mathematical Methods of Physics

Dimensional analysis. Vector algebra and vector calculus. Linear algebra, matrices, Cayley-Hamilton Theorem. Eigenvalues and eigenvectors. Linear ordinary differential equations of first & second order, Special functions (Hermite, Bessel, Laguerre and Legendre functions). Fourier series, Fourier and Laplace transforms. Elements of complex analysis, analytic functions; Taylor & Laurent series; poles, residues and evaluation of integrals. Elementary probability theory, random variables, binomial, Poisson and normal distributions. Central limit theorem.

Mathematical methods are important to anyone who wants to do well in advanced physics. Dimensional analysis is a powerful tool in the hands of a physicist and has helped many people win Noble prize by bringing out new theories for complex problems faced by physicists. Develop the concept of numbers, dimensions and unit along with a good understanding of scale in physics. Space and time scales are important to explain any physical phenomena.

Apart from linear algebra and calculus (start with NCERT), we should be comfortable with certain special functions that always arise in some form whenever we try to solve some real physical problems. Fourier series analysis and integral transforms are tools in the hands of physicist to crack any mathematical situation to easy manipulations and better understanding. Equally important are complex number analysis which help us in a big way.

A new addition is probability theory that is essential to physics, especially experimental physics, statistical mechanics and quantum theory. If you are not comfortable with the elementary ideas, read Statistics text books by NCERT. Especially class XI book is ideal. Central limit theorem and various statistical distributions are important in physics. So have a good understanding of all these.

- NCERT class XI - XII books on Mathematics & Statistics.
- Mathematical Methods for Physicists – Arfken and Weber
- Mathematical Methods for Physicists: A concise introduction - Tai L. Chow (Cambridge University Press - 2000)
- Mathematical Techniques for Engineers and Scientists – Andrews and Phillips (SPIE Press)
- Mathematical Methods for Scientists and Engineers – Donald A. McQuarrie (University Science Books: California)
- Complex Variables – Churchill (McGraw-Hill)
- Mathematical Methods in Classical and Quantum Physics – Tulsi Dass and Satish K. Sharma (University Press – 1998)

### Classical Mechanics

Newton’s laws. Dynamical systems, Phase space dynamics, stability analysis. Central force motions. Two body Collisions - scattering in laboratory and Centre of mass frames. Rigid body dynamics- moment of inertia tensor. Non-inertial frames and pseudo-forces. Variational principle. Generalized coordinates. Lagrangian and Hamiltonian formalism and equations of motion. Conservation laws and cyclic coordinates. Periodic motion: small oscillations, normal modes. Special theory of relativity - Lorentz transformations, relativistic kinematics and mass–energy equivalence.

Not much to say about this basic paper in physics. The main aim is to go from basic laws of Newton to the general principles of Hamilton & Jacobi and through them solve almost all dynamical problems in the classical limits. Learn the tools and solve problems. Canonical transformations are powerful tools. Special relativity should be mastered and is crucial from the exam point of view. You should be comfortable solving all transformation equations and numerical problems in physics.

- Mechanics – Landau and Lifshitz (Pergamon Press)
- Classical Mechanics - R. Douglas Gregory (Cambridge University Press 2006).
- Classical Mechanics – Goldstein, Poole and Safko (Pearson) 3rdEdn.
- Lagrangian and Hamiltonian Mechanics – M. G. Calkin (World Scientific).
- Relativity – The Special and General Theory – A. Einstein.
- Introduction to Special Relativity – R. Resnick (Wiley).

### Electromagnetic Theory

Electrostatics: Gauss’s law and its applications, Laplace and Poisson equations, boundary value problems. Magnetostatics: Biot-Savart law, Ampere’s theorem. Electromagnetic induction. Maxwell’s equations in free space and linear isotropic media; boundary conditions on the fields at interfaces.Scalar and vector potentials, gauge invariance. Electromagnetic waves in free space. Dielectrics and conductors. Reflection and refraction, polarization, Fresnel’s law, interference, coherence, and diffraction. Dynamics of charged particles in static and uniform electromagnetic fields.

Solve Griffiths and you are done! Go topic by topic and not much to avoid here. This is a highly scoring area for those who have the basic knowledge of electromagnetics. Begin with Resnick and Halliday or Kraus and master Griffiths by solving problems. Maxwell’s equations is the milestone but each among the four equations has a story to tell. Differentiate between conducting and non-conducting media and learn about the symmetry of fields and boundaries to be able to solve problems in the area. It is mostly a problem of defining your equations, and solving them using the appropriate boundary conditions. It will be worthwhile to notice that both electric and magnetic fields have many things in common (like both are not conservative fields) but they have fundamental differences (like the presence of electric monopole and absence of magnetic monopole). Fundamentals make good hunting ground for examiners. So be prepared! Also, never forget to look into the relativistic electrodynamics and different gauges used.

Notice the change in the syllabus which now includes some optics which can be had from Hecht. Daniel Fleisch introduces the heart and soul of EMT to an average student through his latest book, have a look at it, if you can. Irodov introduces the concepts of the subject briefly but aptly. It also has several worked out examples and problems.

- Basic Laws of Electromagnetism – I. E. Irodov (Mir Publishers).
- Introduction to Electrodynamics – D. J. Griffiths (Prentice Hall).
- Electromagnetics with Applications – Kraus and Fleisch (McGraw-Hill).
- A Student’s Guide to Maxwell’s Equations - Daniel Fleisch (Cambridge University Press2008).
- Modern Optics – Robert D. Guenther (Wiley - 1990).

### Quantum Mechanics

Wave-particle duality. Schrödinger equation (time-dependent and time-independent). Eigenvalue problems (particle in a box, harmonic oscillator, etc.).Tunnelling through a barrier. Wave-function in coordinate and momentum representations.Commutators and Heisenberg uncertainty principle.Dirac notation for state vectors. Motion in a central potential: orbital angular momentum, angular momentum algebra, spin, addition of angular momenta; Hydrogen atom. Stern-Gerlach experiment. Time-independent perturbation theory and applications. Variational method. Time dependent perturbation theory and Fermi’s golden rule, selection rules. Identical particles, Pauli Exclusion Principle, spin-statistics connection.

Quantum mechanics is the heart of modern physics and some good mathematical concepts along with physical insight will make it interesting. Stick to the basics again and work out basic problems like the calculation of Eigen values, probabilities, expectation values etc. Commutation relations and conservation laws are a must. Remember the solutions to different basic problems like the free particle, one dimensional well, particle in a box and the harmonic oscillator. Angular momentum and coupling are important. Scattering may be difficult to bite but questions could be asked. There are plenty of books available that followsvarious strategies. A book like Modern Quantum Mechanics by Sakurai is quite refreshing, but from the examination point of view it is better to follow more general books considering the demands of the syllabus and examination patterns. Before going to dwell into the following or any serious book, have firm grip of the basics of quantum world using books such as Beiser and Resnick & Halliday.

First three books are sufficient for any level; and both Zttili and Griffiths have several good problems and examples to help you with the exam. If you need a more elaborate and different book, resort to Greiner

- Quantum Mechanics – E. Merzbacher (John Wiley & Sons).
- Quantum Mechanics: Concepts and Applications - Nouredine Zettili, 2nd Edition (John-Wiley, 2009).
- Principles of Quantum Mechanics – R. Shankar (Kluwer Academic/Plenum Publishers).
- Introduction to Quantum Mechanics - David J. Griffiths (Prentice Hall).
- Textbook of Quantum Mechanics - P. M. Mathews and K. Venkatesan (Tata McGraw-Hill).
- Quantum Mechanics an Introduction – Walter Greiner (Springer).
- Modern Quantum Mechanics – J. J. Sakurai.

### Thermodynamic and Statistical Physics

Laws of thermodynamics and their consequences. Thermodynamic potentials, Maxwell relations, chemical potential, phase equilibrium. Phase space, micro- and macro-states. Micro-canonical, canonical and grand-canonical ensembles and partition functions. Free energy and its connection with thermodynamic quantities. Classical and quantum statistics. Ideal Bose and Fermi gases. Principle of detailed balance. Black body radiation and Planck’s distribution law.

It is important to know the basic laws of thermodynamics and the relations that define thermodynamic variables which are obtainable otherwise using the methods of statistical mechanics. It will be better to use books like Pathria and Huang to crack the questions in this section. Develop basic idea of the partition function, ensembles and their classification (put the logic into your mind), and the need for different statistical approaches. The last part is important as we deal with microscopic particles everywhere in physics. It is always helpful if one can draw parallels between different topics in physics and find ways to understand the microscopic origin of macroscopic behaviour. Books # 1 – 4 are for building your basics. I really liked Schroeder.

Mathematical techniques are important to solve all problems in statistical mechanics and so try to work out the appendices of Pathria or any other book that explains those techniques. Your job is done when you are able to obtain the ‘partition function’ of any system that you are considering. One can, in theory, obtain the thermodynamic variables required to understand the system under consideration from the partition function. The partition function depends on whether you have a closed system (canonical ensemble) or an open system (grand canonical ensemble). Have good grasp of probability theory and try to understand how it can be applied to various situations in microscopic systems such as Fermi and Bose systems.

- An Introduction to Thermal Physics – Daniel V. Schroeder (Doring Kindersley India).
- Fundamental of Statistical and Thermal Physics – P. Reif (McGraw-Hill).
- Thermal Physics - Ralph Baierlein (Cambridge University Press).
- Concepts in Thermal Physics - Stephen J. Blundell and Katherine M. Blundell (Oxford University Press 2006).
- Introductory Statistical Mechanics – Bowley and Sanchez (Oxford)
- Statistical Mechanics – R. K. Patria (Butterworth Heinemann).
- Statistical Mechanics – K. Huang (Wiley).
- Elementary Statistical Physics – C. Kittel (John Wiley & Sons).
- Introduction to Modern Thermodynamics - Dilip Kondepudi (John Wiley & Sons).

### Electronics and Experimental Methods

Semiconductor devices (diodes, junctions, transistors, field effect devices, homo- and hetero-junction devices), device structure, device characteristics, frequency dependence and applications. Optoelectronic devices (solar cells, photo-detectors, LEDs). Operational amplifiers and their applications.Digital techniques and applications (registers, counters, comparators and similar circuits).A/D and D/A converters. Microprocessor and microcontroller basics. Data interpretation and analysis. Precision and accuracy. Error analysis, propagation of errors. Least squares fitting.

Any good book covering the syllabus and all probable problems will do for this high scoring part. A good grasp of basic ideas in electronics is a prerequisite. Read books on experimental physics and data analysis (NCERT) to get an idea of the last topics in the syllabus.

- Electronic Devices and Circuits - Bogart, Beasley and Rico.
- Digital Principles and Applications – Malvino and Leech (McGraw-Hill).
- Electronic Principles – A. P. Malvino (Tata McGraw-Hill).
- Operational Amplifiers & Linear Integrated Circuits – R. Gayakawad (Pearson).
- Introduction to Digital Circuits - Theodore F. Bogart.
- Practical Physics - G. L. Squires, Cambridge University Press (2001), 4thEdn.
- An Introduction to Experimental Physics, Colin Cook, Routledge (1996).

## Part ‘C’

### Mathematical Methods of Physics

Syllabus: Green’s function. Partial differential equations (Laplace, wave and heat equations in two and three dimensions). Elements of computational techniques: root of functions, interpolation, extrapolation, integration by trapezoid and Simpson’s rule, Solution of first order differential equation using Runge-Kutta method. Finite difference methods. Tensors. Introductory group theory: SU (2), O (3).

The thrust is on methods to solve differential equations which are crucial to the study of any Physics. I am sure that most of us do computational physics using numerical techniques. Be good at the basics of Taylor’s series expansion. Most numerical methods are improvisation of the Euler’s method. We can expect a problem based on Green’s function method of solving mostly boundary value problems. Finally two important topics in advanced physics come to the fore: Tensors are unavoidable in the study of cosmology and group theory is highly essential in several areas like condensed matter physics, statistical mechanics, quantum theory, spectroscopy and most importantly high energy physics. Books given in part B should be sufficient here as well. Give preference to solving problems in each area and have good basics of tensors and group theory.

### Classical Mechanics

Syllabus: Dynamical systems, Phase space dynamics, stability analysis. Poisson brackets and canonical transformations. Symmetry, invariance and Noether’s theorem. Hamilton-Jacobi theory.

It is not very difficult to cover these topics. Use standard books and try to find the ways to analyse dynamical problems using phase space diagrams. Some hindsight of analytical geometry and calculus will help you here. We can expect good but easily answerable questions from this section. Poisson bracket algebra and canonical transformations are good area of quantitative questions. Symmetry, a consequence of Noether’s theorem, naturally leads to H-J theory and easy analysis of complex problems. Canonical transformations are relevant here as well. One should be comfortable enough to write the equations of motion using the Lagrangian and Hamiltonian approach. Next step is to use the appropriate transformation that will give the Hamiltonian that will be zero, indicating the constant momentum curves in the phase space diagram.

- Classical Mechanics - R. Douglas Gregory (Cambridge University Press 2006).
- Classical Mechanics – Goldstein, Poole and Safko (Pearson) 3rd Edn.
- Lagrangian and Hamiltonian Mechanics – M. G. Calkin (World Scientific).

### Electromagnetic Theory

Dispersion relations in plasma. Lorentz invariance of Maxwell’s equation. Transmission lines and wave guides. Radiation- from moving charges and dipoles and retarded potentials

Workout this section using Griffiths and Jackson(if possible). Give some preference to relativistic dynamics and develop the concepts of Lorentz invariance and gauge invariance. One should be comfortable with the concept of scalar and vector fields and their role in generating electromagnetic disturbances over time and space. These concepts are pretty useful in quantum field theory also.

### Quantum Mechanics

Spin-orbit coupling, fine structure. WKB approximation. Elementary theory of scattering: phase shifts, partial waves, Born approximation. Relativistic quantum mechanics: Klein-Gordon and Dirac equations. Semi-classical theory of radiation

Not much to say about these topics. All are attempts to explain fine results from the labs and some elementary phenomena such as interaction between particles (light too!). We can easily cover these topics using books given in section B above. Try to practice questions based on these sections. A useful book could be the Schaum’s Outlines in Quantum Mechanics which is a good practice book for these topics.

### Thermodynamic and Statistical Physics

First-and second-order phase transitions. Diamagnetism, paramagnetism, and ferromagnetism. Ising model. Bose-Einstein condensation. Diffusion equation. Random walk and Brownian motion. Introduction to non-equilibrium processes.

Not much to cover under this topic. I believe that the important topics in this section are the theory of dia, para and ferromagnetism; Ising model and BE condensation; all available from Patria and Huang. Get a grip of phase transitions from Zemansky and then workout the necessary statistical theory from other advanced books. These are not very easy to digest but worthy of an attempt. Non-equilibrium processes are crucial to many advanced research problems today. Develop a very good understanding of the Diffusion problem starting with statistical and thermodynamic principles and is crucial to many problems in solid state physics and advanced physics problems.

### Electronics and Experimental Methods

Linear and nonlinear curve fitting, chi-square test. Transducers (temperature, pressure/vacuum, magnetic fields, vibration, optical, and particle detectors). Measurement and control. Signal conditioning and recovery. Impedance matching, amplification (Op-amp based, instrumentation amp, feedback), filtering and noise reduction, shielding and grounding. Fourier transforms, lock-in detector, box-car integrator, modulation techniques. High frequency devices (including generators and detectors).

Considering the fact that experimental methods and data analysis are highly desirable for any future experimental physicist, this is beneficial for future researchers in today world of sophisticated experiments. Apart from that we can expect at least one good question from this section. Even though these topics are much beyond the grasp of most postgraduate students in colleges across the country, try to get some knowledge using the books given below or simply get to know about them by visiting the nearest university or Internet. It is often helpful if you can talk to some researcher about the needs for such sophisticated research methods.

- Practical Physics - G. L. Squires, Cambridge University Press (2001).
- An Introduction to Experimental Physics, Colin Cook, Routledge (1996).

### Atomic & Molecular Physics

Quantum states of an electron in an atom. Electron spin.Spectrum of helium and alkali atom. Relativistic corrections for energy levels of hydrogen atom, hyperfine structure and isotopic shift, width of spectrum lines, LS & JJ couplings. Zeeman, Paschen-Bach & Stark effects. Electron spin resonance. Nuclear magnetic resonance, chemical shift. Frank-Condon principle. Born-Oppenheimer approximation. Electronic, rotational, vibrational and Raman spectra of diatomic molecules, selection rules. Lasers: spontaneous and stimulated emission, Einstein A& B coefficients. Optical pumping, population inversion, rate equation. Modes of resonators and coherence length.

This is a section that is much easier to learn and answer. One can expect some numerical calculations based on key fundamental regarding spectroscopic transitions. One has to be thorough with the origin of each region of the electromagnetic spectrum and the explanation offered by atomic and molecular physics to these phenomena. Basic requirements for the study of this topic are quantum mechanics, group theory and some electromagnetic theory.

Books 2 and 3 below can be helpful but if one wants to go more elaborately, Eisberg and Resnick may be helpful. One should be able to answer all questions related to this section, especially from different parts of spectroscopy. Reference #1 will be useful for other sections like Nuclear and Elementary Particle Physics too. J. M. Hollas gives an elaborative description of the subject if one is not content with Barnwell. Those who want some serious laser fundamentals are encouraged to use Silfvast.

- Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, R. Eisberg and R. Resnick (Wiley).
- Molecular Spectroscopy – C. N. Barnwell (McGraw-Hill).
- Modern Spectroscopy - J. Michael Hollas (John Wiley & Sons - 2004).
- Laser Fundamentals – William T. Silfvast (Cambridge University Press - 2004).

### Condensed Matter Physics

Bravais lattices. Reciprocal lattice. Diffraction and the structure factor. Bonding of solids. Elastic properties, phonons, lattice specific heat. Free electron theory and electronic specific heat. Response and relaxation phenomena. Drude model of electrical and thermal conductivity. Hall effect and thermoelectric power. Electron motion in a periodic potential, band theory of solids: metals, insulators and semiconductors. Superconductivity: type-I and type-II superconductors. Josephson junctions. Superfluidity. Defects and dislocations. Ordered phases of matter: translational and orientational order, kinds of liquid crystalline order. Quasi crystals.

This is a crucial paper worth spending time. In physics research, some of the most remarkable results were published in this area. So a good knowledge of the subject not only helps in the exam but also helps in a future career. Develop a good idea about the spatial periodicity which is highly relevant in the case of crystals. Many of their properties can be derived from the harmonic analysis, especially with the help of Fourier analysis. The section include simple theories in crystallography and superconductivity to acoustic and electric properties of matter, free electron theory, heat capacity models, band theory, theory of magnetism, etc.

Knowledge of statistical and quantum mechanics will be highly helpful. Most of the bulk properties are derived from microscopic analysis of matter. It is important to notice that the temperature dependence of many material characteristics such as heat capacity, electrical conductivity, and magnetic properties are obtained through quantum theory using statistical methods. Syllabus follows the contents of Kittel which is the bible of condensed matter physics but not a good text book. It contains the clue to any particular issues in the subject but make judicious use of other books as well. Azhcroft and Mermin give a good account of the Drude model and the electrical, thermal and optical properties of solids.

- Introduction to Solid State Physics – C. Kittel (Wiley)
- Solid State Physics – Ashcroft and Mermin.
- Solid State Physics – Ali Omar (Pearson).
- Problems and Solutions in Solid State Physics – S. O. Pillai (New Age).

### Nuclear and Particle Physics

Basic nuclear properties: size, shape and charge distribution, spin and parity. Binding energy, semi-empirical mass formula, liquid drop model. Nature of the nuclear force, form of nucleon-nucleon potential, charge-independence and charge-symmetry of nuclear forces. Deuteron problem. Evidence of shell structure, single-particle shell model, its validity and limitations. Rotational spectra. Elementary ideas of alpha, beta and gamma decays and their selection rules. Fission and fusion. Nuclear reactions, reaction mechanism, compound nuclei and direct reactions. Classification of fundamental forces. Elementary particles and their quantum numbers (charge, spin, parity, isospin, strangeness, etc.). Gellmann-Nishijima formula. Quark model, baryons and mesons. C, P, and T invariance. Application of symmetry arguments to particle reactions. Parity non-conservation in weak interaction. Relativistic kinematics.

There is not much change from the previous exam here. Only challenge here is the MCQ pattern which demands an objective approach to find the answer. Questions will be based on a detailed problem out of which we have to find possible answers. Nuclear physics, not per se, is not that highly challenging if you go by the exam pattern. Beware in mind that Nuclear Physics is a highly empirical science and much of the theoretical part is available for verification subject to highly sophisticated experiments. High energy reactions mostly deserve relativistic formulations. We can expect both quantitative and qualitative questions from this section. When going through the books we have to double check the fact that there is a constant struggle to explain the experimental evidences which is not quite easy considering the advanced mathematical description of the subatomic world which is invisible to direct human experience. We have to rely upon our intuitions rather than direct visual experience here.

Nuclear models, semi empirical mass formula, nuclear stability, and ideas of different counters can come in handy. In case of reactions and emissions, beta particle decay is important. Follow different mechanisms possible within a nucleus. Elementary particle physics can be tougher for some but learn the classification of particles with the aid of some group theory and general reading. Learn to solve any nuclear or elementary particle reactions using the basic conservation laws used to group them. Hypercharge, Iso-spin, Baryon or Lepton Number, Strangeness, etc., are not that difficult to digest. Ideas of violation of parity, CPT, etc., will help. Questions from this section mostly follow the syllabus and ref. #1 and #2 are very useful to cover the syllabus. One can easily find books that give good coverage of nuclear physics.

- Introduction to Nuclear and Particle Physics – A. Das and T. Ferbel (World Scientific – 2005).
- The Particle Hunters - Yuval Ne’eman and Yoram Kirsh (Cambridge University Press, 1996).
- Subatomic Physics - Ernest M. Henley and Alejandro Garcia (World Scientific, 2007).
- An Introduction to Nuclear Physics – W. N. Cottingham and D. A. Greenwood (Cambridge University Press, 2004).
- Particles and Nuclei: An Introduction to the Physical Concepts – Bogdan Povh et. al. (Springer, 2006).
- Introduction to Elementary Particle Physics – Khanna (Prentice Hall of India).

### Note:

Views expressed here are personal and have no bearings on the policies and practices of either CSIR or UGC.