Quantum Mechanics  

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



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 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



Section 3c: Fine and hyperfine structures

         Non-relativistic expansion

         Spin-orbit interaction

         Darwin term

         Zeeman effects

         Proton-electron spin interaction

         Selection rules

         Contact term



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



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



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 hours:


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.