# Final recommendation of the sub-committee on Bridge Courses

This sub-committee was set up by the SBP, and consists of S. Dugad, S. Gupta (convenor), E. Krishnakumar, V. Nanal, B. Paul, and P. Raychaudhuri. The sub-committee discussed the questions set to it by the SBP (Appendix A) with other members of the departments of physics. Opinions were sought directly or by mail. These opinions were collected and discussed in a meeting on March 24. A further round of consultations with other members of the departments of physics was held and opinons were collected before a second meeting on March 31. All members were present on March 24. B. Paul and P. Raychaudhuri could not attend on March 31.

## Preamble

Currently about a third of all entrants to the graduate school in Physics join without having gone through an M. Sc. course in physics. Most such students have completed a B. Sc., and one or two per year have a B. Tech. degree. Such students often have high levels of skill, but lack some of the background knowledge that the remainder have. The bridge courses are being designed to overcome the consequent practical problems by filling the information gap between the average M. Sc. course in India and the others.

## The nature of the courses

### Recommendations pertaining to the bridge courses per se

- Bridge courses should be divided into modules of 9 classroom contact hours
each. Each such module should carry 1/3 credit units (
*ie*, 3 modules should be equivalent to a core course). Three modules run simultaneously. - Each non-M.Sc. entrant to the graduate school (except B.Tech. in Engineering Physics) is expected to clear a total of 3 credit units from the bridge courses in the first (August-December) semester after joining.
- The bridge courses are additional requirements for the M.Sc. degree in physics over and above the remaining requirements set out in the present rules and regulations of the Subect Board for Physics. As such, grades for the bridge courses shall count towards the said degree.
- Failure to clear the bridge courses will be dealt with as usual under the rules and guidelines of the subject board of physics. Subject to uniform graduate school rules for passing, a student who fails in a particular module in his/her first semester is required to pass it at any time upto his/her third semester.
- Since the bridge courses are only required for an M.Sc. degree, the grades of the bridge courses shall not count towards program allocation for Ph.D. work. In conformity with this rule, overall failure in the bridge courses disqualifies a student from getting an M.Sc. but does not eliminate her/him from the Ph.D. program.
- A student who is otherwise required to take bridge courses may request exemption from one or more modules. Exemption for a module may be granted on the basis of a written examination. If the exemption is granted, then the grade for this examination will count as the grade obtained for the module.
- Students taking bridge courses are expected to join the remainder of their batch for regular course work from the January-April semester. Under normal circumstances they would be ready for program allocation at the end of their third semester.
- After two years of bridge courses, opinions of instructors should be sought about the feasibility of laboratory experiments in these modules.

### Recommendations pertaining to consequential changes in other courses

- The core course on experimental methods should run in parallel to the bridge courses during the first semester and be taken by all students in the batch.
- Since the non-M.Sc. students take the equivalent of four core courses in their first semester, it is fair to expect that the M.Sc. students should take three more core courses (in addition to the common experimental methods course) in this semester.
- In the second semester all students should take the equivalent of four core courses in common. Since it is unusual for Indian students to have any formal exposure to astrophysics and astronomy, it is recommended that there be some form of an introductory course on this subject in the second semester.
- In their third semester the non-M.Sc. students should take the three core courses that they had not taken in their first semester, and take projects or reading courses equivalent to one more core course.

### Recommendations for instructors taking the bridge courses

- The bridge courses are meant to teach M.Sc. level material. Each module is meant to contain theoretical material as well as many applications.
- Each module should be taught by one single instructor. Each instructor can take the help of one student grader.
- The recommended schedule is three hours of classroom instruction per week for 3 weeks followed by an exam in the 4th week.
- The instructor must administer the final exam for a module. If one or more students request tests for exemption, then the instructor must administer a single test to all such students.
- Instructors must cover all the material outlined for each module. The level of detail should be appropriate to the time and intent of the course.
- Instructors can cover all the prescribed material in the module using either the suggested books, or other books in consultation with the course coordinator.
- An instructor shall be deemed to have taught a bridge course even if all students have received an exemption through an examination.

## The content of the courses

The times shown for different parts of a module are recommendations which should also indicate the level of detail intended to be covered.

### Module A:

Classical Mechanics

The Lagrangian and variational equations; symmetries, conserved quantities and Noether's theorem; the Hamiltonian and equations of motion; Poisson brackets, symmetries and Liouville's theorem; the rigid rotator and Euler's equations.

Classical Mechanics

### Module B:

Electricity and Magnetism

Electrostatics: the scalar potential, Laplace and Poisson equations, solution by separation of variables, conformal mappings of a plane; magnetostatics: the vector potential, solutions for several straight wires, the solenoid; dielectrics and the polarisation vector; introduction to Green's functions; the multipole expansion.

Classical Electrodynamics , ch 1-5. Or equivalent chapters of Electricity and Magnetism .

### Module C:

Elementary theory of solids

Ensembles, leading up to quantum ideal gases; Bose and Fermi distributions.
*(4.5 hours)*

Statistical Mechanics I parts of ch 1-5.

The free electron theory of metals; phonons and their contribution
to properties of solids; Bose condensation. *(4.5 hours)*

Solid State Physics , ch 1-3. Or equivalent chapters of Introduction to Solid State Physics .

White dwarfs and the electron degeneracy pressure may be introduced as a further example.

### Module D:

The band structure of crystalline matter

Crystals, lattices and X-ray diffraction; periodic potentials and Bloch's theorem; perturbation theory in weak periodic potentials; bands in one-dimension; the Fermi surface and Brillouin zones; the density of states and van Hove singularities.

Solid State Physics , ch 4-9. Or equivalent chapters of Introduction to Solid State Physics .

### Module E:

The shell models

The Schrodinger equation and bound state problems, leading up to
the Hydrogen atom. *(4 hours)*

Quantum Mechanics , ch 9, 10, or equivalent chapters of any other book.

The atomic shell model: Fermi statistics and the periodic table. Perturbation theory; non-central forces; fine and hyperfine structure; the Helium atom. (4 hours)

Subatomic physics , ch. 14 and 15, and Physical Chemistry , ch 15.

The nuclear shell model: why the magic numbers are different. (1 hour)

Concepts of Nuclear Physics , parts of ch 4, 5.

### Module F:

Quantum Mechanics: applications to spectroscopy

Angular momenta and the rigid rotor; the Wigner-Eckart theorem and
selection rules; the Fermi Golden Rule and transition rates. *(4 hours)*

Quantum Mechanics , ch 16-18. Or equivalent chapters of any other book. (Chapter 9 of , or its equivalent, can be assumed to have been covered in the course on "shell model")

Rotational symmetry breaking: molecular spectra and deformed nuclei. *(4 hours)*

Subatomic physics , ch. 10, 16 and Concepts of Nuclear Physics , ch 5, 6, and Physical Chemistry , ch 16.

Tunnelling and alpha decay. *(1 hour)*

Concepts of Nuclear Physics , ch 10.

### Module G:

Scattering and decays

Reactions and decays; the separation of rates and cross sections
into kinematics and matrix element; non-relativistic and relativistic kinematics;
phase space and Jacobians. *(4 hours)*

Atomic Collisions , ch 1.

Nuclear fission; β-decay of nucleon and muon, including the spectra of
final state particles. *(3 hours)*

Concepts of Nuclear Physics , ch 10, 11. Or Subatomic physics , ch. 11.

Kinematics of 2→2 reactions, Compton scattering, electron-muon scattering,
Bhabha scattering and electron-positron annihilation (matrix elements taken
as given), crossing symmetries. *(2 hours)*

Quarks and Leptons , ch 3-6, and Introduction to Elementary Particles , ch 1-6.

### Module H:

The structure of matter

Symmetries and conserved quantum numbers; rotational symmetry;
antiparticles; discrete symmetries of particle physics: C, P and T; particles and
their quantum numbers; inferring quantum numbers from reactions. *(3 hours)*

Global (internal) symmetries; elements of SU(3) representations; the quark model.
*(6 hours)*

Introduction to Elementary Particles , ch 3-5. (Quarks and Leptons , ch 1-3 contain a part of this material but at a lower level of detail, and hence, if used, must be supplemented by other books.)

### Module I:

Electronics

Voltage, Current and passive circuits (recap) : Constant current and
voltage sources; Thevenin's and Norton's theorem; Equivalent source
resistance; RC integrator, differentiator and filters; Frequency
analysis of a reactive circuit; semiconductors and p-n diode. *(1.5
hour)*

Electronic Principles , ch 1

Transistor basics: npn and pnp transistors; Basic transistor
circuits: Transistor switch, Common-emitter amplifier; Field effect
transistors: JFET and MOSFET characteristics; Transistor amplifier,
Negative feedback; differential amplifier (and its relevance to
op-amps) *(4.5 hour)*

Electronic Principles , parts of ch 6, 7, 8, 10, 12, 13, and 14

Operational Amplifiers: basic OP-amp circuit: linear and non-linear
circuits. *(1.5 hour)*

Electronic Principles , parts of ch 18, 19, 20, 21 and 23

Digital Electronics: Basic logic concepts; Gates and truth tables;
Combinatorial and sequential logic; Karnaugh maps. *(1.5 hour)*

, ch 8

Alternatives to

are andSourendu Gupta. Created on Mar 24, 2005. Last updated on May 02, 2005.