NOTE: Attempt any FIVE questions selecting at least TWO questions from each section.

Section-I (4/9)

Inadequacy of Classical Mechanics

•    Black body radiation

•    Photoelectric effect

•    Compton effect

•    Bohr’s theory of atomic structure

•    Wave-particle duality

•    The de Broglie postulate

•    Heisenberg uncertainty principle

The Postulates of Quantum Mechanics: Operators, Eigenfunctions and Eigenvalues

•    Observables and operators

•    Measurement in quantum mechanics

•    The state function and expectation values

•    Time development of the state function (Schrödinger wave equation)

•    Solution to the initial-value problem in quantum mechanics

•    Parity operators

Preparatory Concepts: Function Spaces and Hermitian Operators

•    Particle in a box

•    Dirac notation

•    Hilbert space

•    Hermitian operators

•    Properties of Hermitian operators

Additional One-Dimensional Problems: Bound and Unbound States

•    General properties of the 1-dimensional Schrodinger equation

•    Unbound states

•    One-dimensional barrier problems

•    The rectangular barrier: Tunneling



Section-II (5/9)

Harmonic Oscillator and Problems in Three-Dimensions

•    The harmonic oscillator

•    Eigenfunctions of the harmonic oscillator

•    The harmonic oscillator in momentum space

•    Motion in three dimensions

•    Spherically symmetric potential and the hydrogen atom

Angular Momentum

•    Basic properties

•    Eigenvalues of the angular momentum operators

•    Eigenfunctions of the orbital angular momentum operators L2  and Lz  

•    Commutation relations between components of angular momentum and their representation in spherical polar coordinates

Scattering Theory

•    The scattering cross-section

•    Scattering amplitude

•    Scattering equation

•    Born approximation

•    Partial wave analysis

Perturbation Theory

•    Time independent perturbation of non-degenerate and degenerate cases

•    Time-dependent perturbations

Identical Particles

•    Symmetric and antisymmetric eigenfunctions

•    The Pauli exclusion principle