Instructor:
E-mail: klikharev@notes.cc.sunysb.edu
Office: Rm. B-135
Phone: 2-8159
Office hours: Thursday 3:00 to 5:00 pm
Preliminary Syllabus:
1. Introduction
Summary of experimental
motivations for quantum mechanics. Basic postulates of wave mechanics; the Schrödinger equation
and its plane-wave solution, the operators of momentum and energy. Discussion:
wavefunction and probability, statistical ensembles, expectation values of
observables. Eigenvalues and eigenstates; example: 1D quantum well. Discrete and continuous spectra. Continuity
equation, probability current.
2. 1D wave mechanics
Plane waves, wave packets. Reflection from a potential step. Tunneling through delta-functional and rectangular barriers.
1D scattering and the transfer matrix. Resonant tunneling. Motion in a periodic
potential; the Bloch theorem, energy bands and gaps. The
WKB approximation, classical turning points, the Bohr-Sommerfeld quantization rule,
the Kemble formula. Propagator, the Feynman path
integral. Harmonic oscillator, the Fock (stationary)
states. Metastable states and their decay.
Rectangular and quasiclassical double quantum wells. Inconvenience of wave
mechanics for those problems.
3. 2D and 3D problems
Generalization to higher
dimensions. 2D and 3D harmonic oscillators, rotators and
spherical quantum wells. Symmetry at rotation, angular
momentum; Bohr’s atom. Partial quantum confinement,
two-slit interference description. Motion in EM field;
the Aharonov-Bohm effect; the Landau levels. 2D and 3D
scattering characterization. The Born approximation,
optical theorem, eikonal approximation. Partial phase
method, hard sphere scattering, resonant scattering.
4.
The bra-ket formalism
Bra and ket vectors. Scalar (inner) product. Linear operators, commutators and anti-commutators. Identity, adjoint and self-adjoint (Hermitian) operators. Compatible and incompatible observables; the uncertainty relation.
Orthonormal sets and matrix formalism. Outer products and projection operators. Change of basis. Matrix diagonalization. The Schrödinger
and Heisenberg pictures of quantum dynamics. The
Ehrenfest theorem. Coordinate operator, reduction to wave mechanics. Revisiting the harmonic oscillator: creation and annihilation
operators, the Fock states, the Glauber (coherent) states, squeezed states.
5. Perturbation theories
Constant perturbation in
non-degenerate and degenerate systems; anharmonic oscillator, the Stark effect.
Time-dependent perturbation theory; the Rabi oscillations.
Transitions in continuous spectrum, the "Fermi Golden
Rule”.
6.
Spin
Insufficiency of wave mechanics. Spin operator; the
Stern-Gerlach experiment and its description. Spin dynamics. Revisiting
the coupled quantum wells. Qubits and quantum
computing. Spin addition to orbital momentum; Clebsh-Gordan
coefficients; Zeeman effect.
7. Open systems, quantum statistics, and
quantum measurements
Coupling to environment. Pure
and mixed quantum states. The density matrix. Classical mixtures in thermal equilibrium. The Wigner
function. Density matrix dynamics without and with interaction with
environment, dephasing. Quantum measurements and ensemble
redefinition. The Bayes theorem.
8. Identical particles
Permutation symmetry,
indistinguishability principle, bosons and fermions. Two-electron
systems, singlet and triplet states, helium atom, covalent (chemical) bond.
Atoms, periodic table of elements. Second
quantization for bosons and fermions, the Fermi gas of interacting electrons.
The Hartri and Hartri-Fock approximations.
9. Quantum theory of EM field
Electromagnetic field modes and
their quantization. The Casimir effect. The notion of photon; its energy, momentum, and angular momentum.
EM field statistics, coherence, 2nd order correlation functions, photon
bunching and antibunching. Quantum EM field interaction with charged particles.
Spontaneous and induced transitions, the electric dipole transition rate, the
Einstein coefficients.
10. Quantum theory of relativistic particles
The relativistic Schrödinger equation,
particles and antiparticles. Dirac equation, introduction of
spin. Relativistic Fermi particles in EM field, spin-orbit interaction,
application to atomic spectra. Relativistic theory of the
hydrogen atom.
11. Quantum field theory concepts
preview
Recommended textbooks:
E. Merzbacher, Quantum
Mechanics, Wiley, 1998
L. Landau and E.
Lifshitz, Quantum Mechanics, Non-Relativistic Theory, 3rd ed.
Pergamon, 1977
J. Sakurai, Modern
Quantum Mechanics, Addison-Wesley, 1994
Lectures:
Twice a week (80 minutes each)
kind
request: be on time
Homeworks:
Weekly (with just a few exceptions)
completed work due: in 7 days
after the assignment
late
submission penalty: 10% a day
Exams:
Two midterm exams (80 minutes
each) and a final (2 hours 30 minutes) each semester
All
exams: books open
Final grade components:
Homeworks: 15%
Midterms:
25+25%
Final
exam: 35%
PHY 511 Logistics
(Fall 2008):
Lectures: Tuesday and Thursday
11:20-12:40 (first lecture: Sep. 2)
room: P-112
Exams (all in the lecture room):
midterms: preliminary, Tuesday Oct. 14 and Tuesday Nov. 11
(lecture time)
final: Thursday Dec. 18 (11:00 am –
1:30 pm)
Grader: Savvas Zafiropoulos
e-mail: savvaslz@gmail.com
room: C-121
office hours: Monday and Wednesday 10:30 to 11:30 am (or by
special appointment via e-mail)
Americans
with Disabilities Act: If you have a
physical, psychological, medical or learning disability that may impact your
course work, please contact Disability Support Services, ECC (
Emergency Evacuation: Students who
require assistance during emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For
procedures and information go to the following website: http://www.sunysb.edu/ehs/fire/disabilities.shtml.
Academic
Integrity: Each student must pursue his or her academic goals honestly and be
personally accountable for all submitted work. Representing another person's
work as your own is always wrong. Faculty are required to report and suspected
instances of academic dishonesty to the Academic Judiciary. For more
comprehensive information on academic integrity, including categories of
academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/ .
Critical Incident Management: Stony Brook University
expects students to respect the rights, privileges, and property of other
people. Faculty are required to report to the Office of Judicial Affairs any
disruptive behavior that interrupts their ability to teach, compromises the
safety of the learning environment, or inhibits students' ability to learn.