Instructor: Konstantin
Likharev
Office:
Physics B-135
Phone: 2-8159
E-mail: klikharev@notes.cc.sunysb.edu
Office
hours: Thursday 4:30 to 6:30 pm
Grader:
Ying Xu
Office:
D-120
Phone:
2-4711
E-mail:
yixu@ic.sunysb.edu
Office
hours: Wednesday 2:00 to 3:00 pm
Web site: http://rsfq1.physics.sunysb.edu/~likharev/308/S06/
Textbook:
ISBN #0-471-0570002 (available in
the campus bookstore)
Additional
D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed.,
R.
L. Liboff, Introductory Quantum Mechanics,
3rd ed., Addison-Wesley, 1998.
Lectures: Mon-Wed-Fri 9:35-10:30 am, Physics
P-116
Homeworks: Weekly (with just a few exceptions)
Exams: Midterm (March 15,
9:35 – 10:30 am) and Final (May 12, 8:00 – 10:30 am)
Grade
Components:
Homeworks:
30%
Midterm:
20%
Final
exam: 50%
Student Feedback: highly appreciated (anonymous notes OK)
Course Syllabus (with approximate
lecture count):
1.
Introduction (5 lectures): Course review. Summary of classical mechanics. Major
experimental foundations of quantum mechanics (Planck’s radiation law, the
photoelectric effect, the Compton effect, electron diffraction, Bohr’s atom).
The de Broglie pilot wave idea.
2.
Free 1D particle (2 lectures): Sine wavefunction. Wavefunction interpretation.
Wave packets, phase and group velocities, packet dispersion and its classical
analog.
3.
1D Schrödinger equation (2 lectures): Free particle description, potential
energy description, momentum operation, Heisenberg’s uncertainty relation,
probability conservation and probability flow. Eigenfunctions and eigenvalues,
the general solution to the Schrödinger equation.
4.
Basic 1D problems (6 lectures): Infinitely deep quantum well, potential step,
potential barrier and tunneling, WKB approximation (without strict derivation),
quantum well of finite depth. Finite-difference method of 1D Schrödinger
equation solution.
5. Dirac’s
δ-function and its applications (6 lectures): Tunneling, resonant
tunneling, weak coupling of quantum wells, metastable state decay. Time-energy
uncertainty relation. Quantum measurements.
6.
Harmonic oscillator (4 lectures): Brute force solution, operator approach,
creation and annihilation operators, coherent (Glauber) states.
7.
Simplest 2D and 3D problems (3 lectures): Schrödinger equation and variable
separation. Infinitely deep quantum well, density of states, quantum mechanics
of classically chaotic systems (semi-qualitatively). 3D numerical methods. Finite-difference method
in higher dimensions.
8.
Motion in central potentials (5 lectures):3D oscillator. 2D rotator. Angular
momentum quantization. Angular momentum in 3D. Spherical harmonics. Dirac’s
(“bra-ket”) notation. Hermite-conjugate and
self-adjoint operators. Derivation of angular quantum numbers.
9.
Orbitals in the hydrogen atom (3 lectures): Main quantum number, energy
spectrum, radial wavefunctions.
10. Spin (2 lectrures): Stern-Gerlach
experiments. Matrix formulation of quantum
mechanics. Spinors and spin operators. Interpretation
of the three-stage SG experiment.