PHYSICS 512 - Quantum Theory and Atomic Structure, II
Section: 001
Term: WN 2013
Subject: Physics (PHYSICS)
Department: LSA Physics
Requirements & Distribution:
Advisory Prerequisites:
Graduate standing. Permission of instructor required.
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
May not be repeated for credit.
Primary Instructor:

This course will focus on the explanation of fundamental concepts, mathematical structure, and calculation methods of quantum mechanics. The course covers the following topics: fundamental concepts of quantum mechanics and its mathematical structure, Exactly solvable quantum systems, symmetries in quantum mechanics, approximation methods, atomic and Molecular structure, scattering theory, quantum many-particle systems, relativistic wave equations.

Course Requirements : There will be regularly assigned problem sets. Your letter grade will be based on the two exams (Midterm 20%; Final: 40%), homework (30%), and class participation (10%).

Prerequisites: The basic mathematical prerequisites are linear algebra and calculus. It would be useful to have a previous course on introductory quantum mechanics at the undergraduate level, but that is not an essential requirement. Some results from group theory will be used for discussion on symmetries, but I will explain the results before I use them.

Books and References

  • P.A.M. Dirac, The Principles of Quantum Mechanics 
  • E. Merzbacher, Quantum Mechanics (1998)
  • J.J. Sakurai, Modern Quantum Mechanics (1982)
Further Readings
  • C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (1997)
  • R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals
  • L. Landau and E. Lifshitz, Quantum Mechanics: Nonrelativistic Theory
  • J. Preskill, Lecture Notes on quantum inforamtion and computation (the first four chapters, which are general quantum mechanics), see


Course Outline: Second term (Winter)

  • Brief introduction and review
  •         Review of the course structure and the first-semester contents
  • Approximation methods in quantum mechanics
    1. Overview of approximation methods in QM
    2. Time-independent perturbation methods
      • The general method and classification of perturbation theory
      • Bound-state non-degenerate perturbation
      • Basic recursion relations for arbitrary order perturbation, explicit formula for 1st and 2nd order perturbation
      • The degenerate perturbation method
      • Convergence, asymptotic series, and limit of perturbation theory
    3. Example applications of the time-independent perturbation
      • d.c. Stark shift (from a static electric field) of the ground state of the hydrogen-like atoms (non-degenerate perturbation)
      • d.c. Stark shift of excited states of the hydrogen-like atoms (degenerate perturbation)
      • Atom's polarizability and atom's trap
      • a.c. Stark shift (from a laser) of the ground state of the hydrogen-like atoms
      • Design of optical lattice from a.c. Stark shift
    4. Time-dependent perturbation, transition, and Fermi's golden rule
      • Time-dependent perturbation (formalism)
      • Time-energy uncertainty relation
      • Fermi's golden rule for transition (discrete spectrum to continuous spectrum)
      • Atomic transition through broadband incoherent (thermal) light
      • Stimulated emission and absorption, explain of spontaneous emission
      • Quantum Zeno effect (coherent vs incoherent transitions)
    5. The variational method
      • The general idea
      • The variational principle for the stationary Schrodinger equation
      • The variational principle for the dynamical Schrodinger equation
      • A simple illustrative example: Harmonic potential
    6. Example applications of the variational method
      • The ground state of the Helium-like atoms
      • The band-gap structure for atoms in the optical lattice
      • Quantum phase transitions in quantum magnetism: mean-field theory for the anisotropic Heisenberg model
    7. The semi-classical (WKB) method
      • The WKB approximation
      • Turning points and the connection formula
    8. Example applications of the WKB method
      • Quantization condition for a single-minimum potential
      • Quantization condition and the eigen-energies of the double-well potential
      • Tunneling through any potential barrier
    9. The adiabatic approximation and the Berry's phase
      • The fast and slow evolution: sudden versus adiabatic approximation
      • The adiabatic theorem and the Berry's phase
      • Proof the adiabatic theorem, dynamical and Berry's (geometric) phase, Estimation of the transition probability
      • The adiabatic passage with counter-intuitive pulses
      • The adiabatic quantum algorithm
      • The Berry's phase for a two-level system
  • Structure of atoms and molecules
    1. Overview
      • Overview of the atomic and molecular structure
      • About the units
    2. Fine structure of the hydrogen-like atoms
      • Spin-orbital coupling
      • Splitting of the energy levels due to the spin-orbital coupling
      • The relativistic correction to eigen-energies and the whole fine structure
    3. The hyperfine structure of the hydorgen-like atoms
      • The basic picture
      • The hyperfine coupling Hamiltonian
      • N, L coupling, N,S coupling (contact vs. dipole terms)
      • The hyperfine splitting of the ground state
      • Level splitting, applications in radio astronomy
    4. Influence of magnetic fields on atomic structure: Zeeman effects
      • Atomic magnetic moment
      • Zeeman effects within Fine structure
      • Zeeman effects within hyperfine structure
    5. The molecular structure
      • The Born-Oppenheimer approximati

PHYSICS 512 - Quantum Theory and Atomic Structure, II
Schedule Listing
001 (LEC)
TuTh 11:30AM - 1:00PM
NOTE: Data maintained by department in Wolverine Access. If no textbooks are listed below, check with the department.

Please refer to for more information about textbooks,etc.
ISBN: 9780131461000
Quantum mechanics, Author: Ernest S. Abers., Publisher: Pearson Education Inc. 2004
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