**Quantum Mechanics **

**(Spring 2007, 4 credits, M, Th, 8.00-9.50am)**

**Syllabus:**

**Section
1: Spin**

•
Particle intrinsic spin

•
“Motionless” spin particle

•
Spin particle in motion: spinors

•
Rotational operator

•
Spin dynamics

**Section 2a:** **Spin addition **

• Two interacting spins

•
Addition of two spin ½ angular m

• Dynamics of spin interactions

**Section 2b:** **Angular m omentum
addition-general **

• Number of degeneracies

• Coupled representations

• Clebsch-Gordon coefficients

•
Wigner-Eckart

**Section 3a:** **Approximation: variation method**

• Variational principles

• Born-Oppenheimer approx

• Non-central fields

•
Periodic potential

•
WKB approximation

**Section 3b: Approximation: perturbation **

• Stationary perturbation

• Perturbative expansion

• Degenerate perturbation

• Examples

**Section 3c:** **Fine and hyperfine structures**

• Non-relativistic expansion

• Spin-orbit interaction

•

• Zeeman effects

• Proton-electron spin interaction

• Selection rules

• Contact term

• Positronium

**Section 4: Time dependent perturbation **

• Transition probability

• Fermi-Golden rules

• Resonance interaction

•
At

• Dipole and quadruple interaction

• Adiabatic processes

• Aharonov-Bohm Effect

**Section 5a:** **Quantum scattering I (Born approx.) **

• Cross section

•
Stationary state so

• Green function

• Scattering amplitude

• The Born approximation

• Applications

**Section 5b:** **Quantum scattering II (Partial waves) **

•
Angular m

•
Plane waves in terms of angular m

•
Partial waves in *V(r)*

• Phase shift and cross section

• Applications

**Section 6: Relativistic quantum mechanics**

• Relativistic single particle theories

•
So

• Dirac equation: in EM field

• Dirac equation: covariant form

**Section 7a: Classical
fields**

- Discrete infinite
degree of freedom

• System of harmonic oscillators

•
Continuous infinite degree of freed

•
Field equations and Lagrangian density

•
Hamiltonian density

**Section 7b: Quantization of
fields**

- Hamiltonian of a
quantum field
- Quantization of EM fields
- Interaction of EM
fields with atoms
- Spontaneous emission
- Gauge invariance and
Dirac fields

Instructor: Professor T.-M. Lu (

Office: CII 6015; Tel:
x2979

Office hours:

TA: to be named (for homework and inclass)

Office:

Office hours:

Grades:

in-class:
10% (checked by TA)

homework: 15% (checked by TA. No late homework, solutions

posted
in

midterm:
30% (5-8pm, March 15)

final: 45%

•
Take class attendance: no late attendance

•
Written notice from doctor is required if sick (
to Dr.

Lu and cc to TA) for any missing
class

Text
book: Principles of Quantum Mechanics

(Second Edition, R.Shankar,
Springer)

(Bring your book every class)

Class
notes: will send you.