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

Part A. Elemen= ts of Quantum Mechanics

1. Quick review of modern matter wave experiments

2. Basic Principle of Q.M.

Hilbert space; Time evolution operator; Measurements<= /span>; Complete set of commuting observab= les

3. Photon polarization (Le Bellac, chapter 3)<= /span>

Classical polarization; Jones vector; polarization of a photon; projection operator.<= span style=3D'font-size:14.0pt;mso-bidi-font-size:11.0pt;line-height:115%'>=

4. Quant= um cryptography

5. Spin = 1/2 systems

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

6. Densi= ty operator/State Operator (La Bellac)<= /span>

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

7. Entan= gled states (La Bellac, chapter 6)=

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

8. The E= PR paradox and the Bell Inequality

EPR thought experiment; Resolving EPR paradox; Quantum Information

9. Quant= um Computing and Quantum Teleportation

Hadamard gate and CNOT gate<= /span>

Part B. Schrodinger Quantum Mechanics

1. Some formal quantum mechanics

General Heisenberg uncer= tain relation; Time evolution operator

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

Constant B field; princi= ple 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. Spre= ading of a wave packet in free space

2. 1D Harmonic oscillator—operator formulation<= o:p>

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

** students are assumed to be familiar wi= th 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 oscilla= tor (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

<= span style=3D'mso-list:Ignore'>5.&n= bsp; Charged particles in an EM field; Gauge Invariance= (Merz. P71-77)

Part D. Three-dimensional Problems

1. Orbit= al Angular momentum

2. Algeb= raic approach to angular momentum

3. Addit= ion of angular momentum