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
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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/
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