Physics 623: Quantum Mechanics II
TextBook: Landau L.D., Lifshitz E.M., Quantum Mechanics, Non-Relativistic Theory (3ed.,
Pergamon, 1991)
Course outline: The goal of this theoretical course is to introduce techniques in two of
the most widely used application areas of Quantum Mechanics, namely Scattering Theory
and Many-Body Physics. A working knowledge of these methods is particularly relevant
to a wide range of modern applications in the broad area of mesoscopic physics, and
especially to studies involving ultra-cold atoms.
Topics covered are:
1. Scattering theory
i) Role-players: scattering amplitude, T-matrix, Green’s function
ii) Partial waves
iii) Unitarity
iv) Low-energy scattering: scattering length and the Fermi-Huang potential
v) Resonant scattering
vi) Scattering at high energies
vii) Scattering of identical particles
2. Second quantization
i) Permutation symmetry
ii) Second quantization: Bose statistics
iii) Second quantization: Fermi statistics
iv) Bosonic and fermionic atoms in optical lattices
v) Munich experiment and the simulation of solid state systems using atomic means
3. Atomic theory
i) Spin; the spin operator
ii) Spinors
iii) Exchange interaction
iv) Atomic energy levels
v) Electron states in an atom
vi) The Thomas-Fermi equation revisited
vii) Fine structure
viii) Periodic table
ix) Excitation spectra
Pre-requisites: Physics 613: Quantum Mechanics, Atomic and Molecular Physics
Physics 616: Mathematical Methods for Physicists
Homework: There will be four homework assignments.
Exams: There will be one mid-term exam, and one final exam.
Grading: The total grade will consist of: assignments 30%, mid-term exam 20%, final exam
50%.
Example of additional references:
M.P.A. Fisher, P.B. Weichman, G. Grinstein, and D.S. Fisher, "Bose localization and the
superfluid-insulator transition", Phys. Rev. B 40, 546 (1989)
D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold Bosonic Atoms in Optical
Lattices”, Phys. Rev. Lett. 81, 3108 (1998)
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, and I. Bloch, “Quantum phase transition
from a superfluid to a Mott-insulator in a gas of ultracold atoms”, Nature 415, 39 (2002).
STATEMENT ON DISABILITY ACCMMODATIONS:
Section 504 of the Americans with Disabilities Act of 1990 offers guidelines for
curriculum modifications and adaptations for students with documented disabilities. If
applicable, students may obtain adaptation recommendations from the Ross Center for
Disability Services, M-1-401, (617-287-7430). The student must present these
recommendations and discuss them with each professor within a reasonable period,
preferably by the end of Drop/Add period.
STUDENT CONDUCT
The Code of Student Conduct provides a framework of standard acceptable behavior for
students. It is set forth to give students general notice of prohibited conduct; it should not
be regarded as an exhaustive definition of misconduct or construed as a contract between
the student and the University. Students are responsible for understanding and complying
with this Code. Copies of the Code of Student Conduct are available in the Office of the
Vice Chancellors for Academic and Student Affairs, in the undergraduate catalog and
graduate bulletin, in the UMass Boston Student Handbook, and on the University's
website.
http://www.umb.edu/life_on_campus/policies/code/