Physics 460
Quantum Mechanics II
Luming Duan
Winter 2017
Welcome to the course homepage of the
physics 460! This is the secondsemester undergraduate quantum mechanics.
Course Description
This course will focus on the explanation of concepts and
methods of quantum mechanics and their applications. The course will cover the
following topics: review of formalisim of quantum
mechanics, finitedimensional quantum dynamics and its applications, perturbation
theory and its applications, atomic and molecular structure, variational method and its applications, the WKB
approximation and the adiabatic theorem, scattering theory.
Class meetings
Time: Tuesday, Thursday, 11:30AM 1:00PM
Location: 335WH (West Hall)
Instructors
Luming Duan
4219 Randall Hall
Telephone: (734) 7633179
Email: lmduan@umich.edu
Web: http://wwwpersonal.umich.edu/~lmduan/
Course website: http://wwwpersonal.umich.edu/~lmduan/QMunder460pub17.html
Office hours: I am in office most of the time, you may just stop by,
or you can send an email for an appointment.
Teaching assistant (Grader): Zhengyu Zhang (Randalll 4218)
Course Requirements
There will be regularly assigned problem sets. Your letter
grade will be based on two exams (Midterm 25%; Final: 35%,), homework (30%),
and class participation (10%).
Prerequisites
The basic mathematical prerequisites are linear algebra and
calculus. I also assume that you have taken quantum mechanics I (physics 453 or
equivalent).
Books and References
Textbook


Introduction to Quantum Mechanics.

Other
recommended
textbooks


 J.J. Sakurai, Modern
Quantum Mechanics (1982)
 C. CohenTannoudji, B. Diu, and F. Laloe,
Quantum Mechanics (1997)
 S. Gasiorowicz,
Quantum mechanics
 E. Merzbacher,
Quantum Mechanics (1998)

Further Readings
recommended


 P.A.M. Dirac, The
Principles of Quantum Mechanics
 R. P. Feynman, the
Feynman lectures on physics III
 M. Born, Atomic
physics
 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
http://www.theory.caltech.edu/people/preskill/ph229/#lecture

Course Outline
 History and perspective of
quantum mechanics
 History and
development of quantum mechanics
 Structure of this
course
 Review of formalism of
quantum mechanics (Lecture Notes,
reference Griffiths Chapter 3 and 12.3)
 states, evolution,
and measurements
 States in QM
 Observables in QM
 Evolution in QM
 Example application:
quantum nocloning theorem
 Measurements in QM
 Example application:
Quantum cryptography
 Finitedimension
vs. continuousvariable quantum systems
 Examples of
finitedimension physical systems
 Description of
2dimensional (qubit) systems
 Continuousvariable
systems
 Coordinate and
momentum basis representations
 Uncertainty
relation, Schrodinger versus Heisenberg pictures
 Uncertainty relation
 Evolution in the
Schrodinger picture
 Evolution in the
Heisenberg picture
 Example application
of the Heisenberg equation: quantum dispersion
 Quantum dynamics of
twodimensional systems and its applications
 Evolution of
2dimensional (qubit) systems: Rabi oscillation
 Atomic clocks and the
Ramsey method
 Neutrino oscillation
 Multipartite quantum
systems, density matrix, and quantum entanglement
 Multipartite quantum
systems
 Density
matrix/operator
 Properties of the
density matrix
 Quantum entanglement
and von Neumann entropy
 Perturbation theory (Lecture Notes,
reference Griffiths Chapter 6.1,6.2 and 9)
 Overview:
classification of perturbation theory
 Timeindependent
perturbation methods
 The general method
 Nondegenerate
perturbation (1st and 2nd order)
 The degenerate
perturbation method
 Combination of
degenerate and nondegenerate perturbation, examples
 Stark effect and
optical lattice
 Brief review of the
hydrogen structure
 d.c.
Stark shift
 a.c.
Stark shift and optical lattice
 Timedependent
perturbation theory and Fermi's golden rule
 Timedependent
perturbation
 Fermi's golden rule
 Atomic transitions,
selection rules, and quantum Zeno effect
 Atomic transitions through
incoherent light
 Selection rules
 Quantum Zeno effect
(coherent vs. incoherent evolution)
 Variational method
and its applications (Lecture Notes,
reference Griffiths Chapter 7)
 Overview
 The variational method
 The general idea
 The variational principle for the Schrodinger equation
 An example: Harmonic
potential
 Applications of the variational method
 The Heliumlike atoms
 Quantum phase
transitions in quantum magnetism: meanfield theory
 The semiclassical
(WKB) method and the adiabatic theorem (Lecture Notes,
reference Griffiths Chapter 8 and 10)
 The semiclassical
(WKB) method
 The WKB approximation
 Quantization
condition under infinite wells
 Turning points and
the connection formula
 Applications of the
WKB method
 Quantization
condition for a general potential
 Tunneling through a
potential barrier
 Example: theory of
alpha decay
 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
 Applications of the
adiabatic approximation
 The adiabatic passage
for quantum control
 Adiabatic quantum
computation
 The Berry's phase for
a twolevel system
 Structure of atoms and
molecules (Lecture
Notes, reference Griffiths Chapter 6.36.5)
 Overview
 Fine structure of the
hydrogenlike atoms
 The relativistic
correction
 Spinorbital coupling
 Energy correction due
to the spinorbital coupling
 The hyperfine
structure of the hydorgenlike atoms
 The basic picture of
coupling
 The hyperfine
splitting of the ground state
 Atomic structure under
magnetic fields: Zeeman effects
 Hamiltonian under a
magnetic field
 Zeeman effects
 The molecular
structure
 The general picture
and the BornOppenheimer approximation
 The molecular
hydrogen ion
 The electronic
structure
 Vibrational and
rotational levels
 Scattering theory (Lecture Notes,
reference Griffiths Chapter 11)
 Partialwave expansion
 General picture of
scattering
 Partialwave
expansion
 Unitarity
and the collision phase shift
 How to solve the
collision phase shift
 The LippmannSchwinger
equation and the Born approximation
 The Green's function
 The
LippmannSchwinger (LP) equation in the coordinate basis
 The cross section
from the LP equation
 The Born
approximation
 Applications of the
Born approximation
Links