Instructor:
E-mail: klikharev@notes.cc.sunysb.edu
Office: Rm. B-135
Phone: 2-8159
Office hours: Thursday 1:30 to 3:30 pm
Preliminary Syllabus:
1. Introduction (lecture
notes)
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. Partial quantum
confinement, reduction to 2D and 1D.
2. 1D wave mechanics (lecture
notes – Sec. 2.5 still in a draft form)
Plane waves, wave packets, propagator. Reflection from a
potential step. Tunneling through a rectangular
barrier. The WKB approximation, connection formulas for classical
turning points, the Bohr-Sommerfeld quantization rule. Delta-functional
barriers and quantum wells. 1D scattering and the
transfer matrix. Resonant tunneling; metastable states
and their decay. Motion in a periodic potential; the
Bloch theorem, energy bands and gaps; weak-coupling and tight-binding
approximations. The brute force approach to the
harmonic oscillator problem.
3. 2D and 3D problems of wave mechanics (lecture notes).
Density of states. Two-slit interference description.
Motion in EM field; the Aharonov-Bohm effect; the Landau levels, the quantum
Hall effect. 2D and 3D scattering
characterization. The Born approximation, ways toward
improvement. Elements of the multi-dimensional band
theory. 2D and 3D harmonic oscillators, 2D and 3D
rotators, circular and spherical quantum wells, the Bohr atom. Insufficiency of wave mechanics.
4.
The bra-ket formalism and applications
(lecture notes)
Motivations; the Stern-Gerlach experiment. Bra and ket
vectors. Scalar (inner) product. Linear operators, commutators and anti-commutators. Identity, adjoint and self-adjoint (Hermitian) operators. Outer products and projection operators. Orthonormal
sets and matrix formalism. Change of basis and matrix diagonalization.
Spin operator; the Stern-Gerlach experiment’s description. Compatible
and incompatible observables; the uncertainty relation. Quantum dynamics in the Schrödinger and Heisenberg pictures.
Spin precession. Continuous spectrum, coordinate operator,
reduction to wave mechanics; the Ehrenfest theorem. Coordinate
and momentum representation of wave packets. The
Feynman path integral. Revisiting the 1D harmonic oscillator:
creation and annihilation operators, the Fock states, the Glauber (coherent)
states, squeezed states. Revisiting the angular momentum;
ladder operators.
5. Perturbation theories and applications (lecture notes)
Constant perturbation in
non-degenerate and degenerate systems; anharmonic oscillator. Coupled quantum wells. The Stark effect.
Spin addition to orbital momentum; Clebsh-Gordan coefficients; Zeeman effect. Time-dependent perturbation
theory; the Rabi oscillations. Transitions in
continuous spectrum, the "Fermi Golden Rule”.
6. Open systems, quantum statistics, and
quantum measurements (lecture notes, with sections 6 and 7 in
a draft form)
Coupling to environment. The density matrix.
Pure and mixed quantum states. Classical
mixtures in thermal equilibrium. The Wigner function. Density
matrix dynamics without and with interaction with environment. Energy relaxation and dephasing. Quantum
measurements and ensemble redefinition.
7. Multiparticle systems (lecture
notes, with a part of Sec. 3 still missing)
Permutation symmetry, indistinguishability
principle, bosons and fermions. Two-electron systems, singlet and triplet
states, helium atom. Atoms, periodic table of elements. Second quantization for
bosons and fermions, the Hubbard model, the Fermi gas of interacting electrons.
The Hartri and Hartri-Fock approximations; density functional theory.
8. Electromagnetic field quantization (lecture notes)
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.
9. Quantum theory of relativistic particles (lecture notes - just bits and pieces)
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.
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)
Homeworks:
Weekly (with just a few exceptions)
Exams:
A midterm exam (80 minutes)
and a final (2 hours 30 minutes) each semester
all
exams: books open
Final grade components:
Homeworks: 25%
Midterm:
30%
Final
exam: 45%
PHY 512 logistics (Spring 2009):
Lectures: Tuesday and Thursday 9:50-11:10
Room: P-113
Exams (all in the lecture room):
Midterm:
Tuesday March 17 (lecture time)
Final:
Tuesday May 19 (8:00 – 10:30 am)
Grader: Ionel Patu
E-mail:
ipatu@grad.physics.sunysb.edu
Office:
M 6-114
Office
hours: Wednesday 2 to 3 pm, or by e-mail appointment
Homework
submission deadline: Friday 3:00 pm
Late
submission policy: off 10% a day, until next Wednesday morning
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.
PHY 511 homeworks and optional
problems:
Optional problems Set 1
with solutions
Optional problems Set 2 with solutions
PHY 511 Exams:
PHY 512 homeworks and optional
problems:
Optional problems Set 3
with solutions
Optional problems Set 4
with solutions
PHY 512 Exams:
NEW: Final exam
with solutions