Phys 943: Quantum Mechanics Instructor: Silas Beane
Office: DEM 209E
Phone: 603-862-2720
email:
silas@physics.unh.edu web: http://www.physics.unh.edu/~silas
Office hours: Thursday 12:30-1:30 pm, Friday 12-1pm
I strongly encourage students to communicate with me by email for
bureaucratic issues. At times, I'll communicate with the class by email.
Please, no physics questions via email!
If necessary, you may visit me outside of office hours but please do
not be offended if I'm unable to speak with you immediately.
The grades for this course will be based on homeworks (60%) and the final exam at the end of the semester (40%). The final exam will be comprehensive; there will be no mid-term tests.
You will have two weeks to complete each homework set; there will be
seven homework assignments. The homeworks will be long and
difficult. If you start working on an assignment the day before
it's due, you will not finish it in time. Late homeworks will not be
accepted unless there is a compelling rationale.
I encourage you to work on the homework in groups. However, you must list your collaborators on
your
manuscript.
There will be one homework in the middle of the semester with no
collaboration allowed.
I believe that most of what you'll get out of this class will be
from the homeworks. Due to the large amount of material that must be
covered, generally I will present the theoretical
formalism and the worked problems will be left to the homework.
Some useful texts
(on reserve in the library)
C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics
L.D. Landau and E.M. Lifschitz, Quantum Mechanics
(Non-relativistic theory)
E. Merzbacher, Quantum Mechanics
R. Shankar, Principles of Quantum Mechanics
A. Messiah, Quantum Mechanics
Gradshteyn and Ryzhik: Table of Integrals, Series, and
Products
A. Das and A.C. Melissinos: Quantum Mechanics: A
Modern Introduction
A. Bohm: Quantum Mechanics: Foundations and Applications
A.S. Davydov: Quantum Mechanics
A.P. French and E.F. Taylor: Introduction to Quantum
Physics
R. Feynman: The Feynman Lectures on Physics
Calendar (topics covered & homework)
| Week | Monday | Wednesday | Friday | HW (due on Fridays) |
| 1. 1/19 | MLK Day |
Introduction The two-slit experiment The Stern-Gerlach experiment |
HW1(ps,pdf) |
|
| 2. 1/26 | Linear vector spaces Bras, kets and operators Projectors |
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| 3. 2/2 | Matrix representations Measurements (In)Compatible observables |
HW2(ps,pdf) HW1 due |
||
| 4.
2/9 |
The uncertainty
principle Change of basis Continuous spectra Position eigenkets Translation operator/ momentum Position-momentum uncertainty |
|||
| 5. 2/16 | Wavefunctions Guassian wavepackets Mixed states and density matrices |
HW3(ps,pdf) HW2 due |
||
| 6. 2/23 | Density matrices Time evolution Spin 1/2 system in a magnetic field Time-energy uncertainty |
|||
7. 3/1 |
Schrodinger vs.
Heisenberg pictures Time-dependence of operators and matrix elements Ehrenfest's theorem 1-d harmonic oscillator |
HW4(ps,pdf) notes(ps,pdf) HW3 due |
||
| 8. 3/8 | 1-d wave mechanics Generic potential Classical limit Leading order WKB |
No
class Friday |
||
| 9. 3/15 | Spring Recess |
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10. 3/22 |
Leading order WKB (cont.) The step potential The infinite potential barrier Rectangular potential barrier and the S-matrix |
HW5(ps,pdf) HW4 due Midterm Chart (ps,pdf) |
||
| 11. 3/2 | No class Monday |
Propagators Green's functions Path integral formulation |
||
12. 4/5 |
Potentials in quantum
mechanics U(1) symmetry and electrodynamics Aharonov-Bohm effect and the topology of the vacuum |
HW6(ps,pdf) HW5 due |
||
13. 4/12 |
Rotations in 2-d SO(2), its generator, and its representations Angular momentum |
|||
14. 4/17 |
Rotations in 3-d The Euler angles SO(3) in quantum mechanics |
HW7(ps,pdf) HW6 due |
||
15. 4/26 |
D-matrices d-matrices, j=1/2,1 Orbital angular momentum Spherical harmonics |
|||
16. 5/3 |
Addition
of angular momenta Clebsch-Gordan Coefficients Vector and tensor operators |
No class Wednesday |
(double
class Friday) |
HW7 due |
17. 5/10 |
Wigner-Eckart theorem Projection theorem |
Reading Days |
FINAL EXAM (ps,pdf) Final Chart (ps,pdf) |
|