Detailed write-up of the contents in QMI (S2008)

Part A.  Elements  of Quantum Mechanics

1.     Quick review of modern  matter wave experiments

2.     Basic Principle of Q.M.

Hilbert space; Time evolution operator;  Measurements;  Complete set of commuting observables

3.     Photon polarization (Le Bellac, chapter 3)

Classical polarization; Jones vector; polarization of a photon; projection operator.

4.     Quantum cryptography

5.     Spin 1/2 systems

Stern-Gerlach experiment; spin state of arbitrary orientation; Pauli matrices; rotation of spin 1/2  states;

6.     Density operator/State Operator (La Bellac)

Pure states; mixed states; spin polarization; dynamics and time evolution; time-dependence of state operator;

7.     Entangled states (La Bellac, chapter 6)

Two spin 1/2 systems; product space; reduced state operators.

8.     The EPR paradox and the Bell Inequality

EPR thought experiment; Resolving EPR paradox; Quantum Information

9.     Quantum Computing and Quantum Teleportation

Hadamard gate and CNOT gate

Part B. Schrodinger Quantum Mechanics

1.     Some formal quantum mechanics

General Heisenberg uncertain relation; Time evolution operator

2.     Two-level problems—spin 1/2 particles in a magnetic field

Constant B field; principle of the NMR; detuning and resonances;

3.     Two-level problems  II

Ammonia masers; neutrino oscillation; kaons

4.     Systems with finite number of levels

Molecular orbitals of C2H2, H2+, benzene

Part C. Practical methods of solving Schrodinger equation –Quick review of some 1D problems

1.      Spreading of a wave packet in free space

2.     1D Harmonic oscillator—operator formulation

Creation and annihilation operators; motion of a wave packet; coherent and squeezed states

** students are assumed to be familiar with these problems at the level of Griffths and can use Mathematica to solve problems.

For bound states, they know how to solve: infinite square well, finite square well; delta-function potential; harmonic oscillator (Chapter 2 of Griffths). They also know variational method and simple perturbation theory(Griffths 6.1 and 6.2) . For continuum states, they are familiar with scattering from steps, wells.

3.     Resonances, phase shift, time delay and scattering matrix in 1D scattering  (Merz. p97, p108)

4.     Density of states and periodic boundary conditions (Merz. P64)

Including quantum dots, quantum well, quantum wire

5.     Charged particles in an EM field; Gauge Invariance (Merz. P71-77)

Part D. Three-dimensional Problems

1.     Orbital Angular momentum

2.     Algebraic approach to angular momentum

3.     Addition of angular momentum