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 momenta

•         Dynamics of spin interactions

 

Section 2b: Angular momentum addition-general

•         Number of degeneracies

•         Coupled representations

•         Clebsch-Gordon coefficients

•         Wigner-Eckart Theorems

 

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

•         Darwin term

•         Zeeman effects

•         Proton-electron spin interaction

•         Selection rules

•         Contact term

•         Positronium

 

Section 4: Time dependent perturbation

•         Transition probability

•         Fermi-Golden rules

•         Resonance interaction

•         Atom in EM radiation

•         Dipole and quadruple interaction

•         Adiabatic processes

•         Aharonov-Bohm Effect

 

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

•         Cross section

•         Stationary state solutions

•         Green function

•         Scattering amplitude

•         The Born approximation

•         Applications

 

Section 5b: Quantum scattering II (Partial waves)

•         Angular momentum free space solutions

•         Plane waves in terms of angular momentum

•         Partial waves in V(r)

•         Phase shift and cross section

•         Applications

 

Section 6: Relativistic quantum mechanics

•         Relativistic single particle theories

•         Solution of Dirac equation: free particle

•         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 freedom

•         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 (lut@rpi.edu)

                        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 Huntington lab at 12.00pm)

            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.