Wave Mechanics I and II (PHY 4604 and 4605)
or equivalent. The course is aimed at first-year graduate
students majoring in physics, optics, chemistry, electrical
engineering, and
materials science. Undegraduate students interested in taking this
course should consult with the instructor beforing registering.
Content:
1)
Mathematics
of
Quantum Mechanics: Linear vector spaces,
internal product. Dirac notation. State vectors and operators. Matrix
notation. Transformations. Eigenvalue problems. Functionals.
Generalization to infinity dimensions.
2) Revision of Classical Mechanics:
Lagrangian formulation and the principle of minimal action. Hamiltonian
formalism. Cyclic coordinates, Poisson brackets. Canonical
transformations. Symmetries.
3)
Postulates
of Quantum Mechanics: Classical
× Quantum mechanics. Postulates.
Interpretation. Experimental tests. Schrödinger equation.
Evolution operator.
4)
One-dimensional
Applications: Free particle. Particle in a box. Boundary
conditions. Stationary states. Piecewise constant potentials.
Continuity equation for probability. Gaussian packets.
5)
Harmonic
Oscillator: Motivation. Classical oscillator. Quantization in
the space representation. Quantization in the energy representation.
Creation and
annihilation operators.
6)
Classical Limit: Expectation values.
Ehrenfest theorem.
7)
Heisenberg uncertainty relations: Derivation. Minimum
uncertainty states. Applications.
8)
Symmetries in Quantum Mechanics:
Translation invariance in space. Translation invariance in time.
Parity. Time reversal.
9)
Rotation Invariance and Angular Momentum:
Two-dimensional problem. Eigenvalues of
Lz.
Angular momentum in three dimensions. Eigenvalues of
L2
e Lz. Central
potentials. Hydrogen atom. Spin.
Textbook:
Principles of Quantum Mechanics, 2nd edition, by R.
Shankar (Plenum Press, 1994).
Another useful book for this course is
Modern Quantum Mechanics,
2nd edition, by J. J. Sakurai (Addison-Wesley, 1994).
Grading: Final grades will be based on homework (1/3), a
mid-term (1/3), and an end-term exam (1/3). Problem sets will be handed out
every two weeks. Grading will be done over a scale from 0 to 100. Final
letter grades will be given according to the following grid: A
(100-90), B (89-75), C
(74-60), D (59-50), and F (49-0). +/- may be used. Problem sets
handed in after the due date will be devaluated in 10% for every late
day. The tentative day for the mid-term exam is October 12 (Friday).
The final exam has been schedule for December 10 (Monday), from 10:00 am -
12:50 pm in MAP 306.
CALENDAR
PROBLEM SETS (pdf files)
#1 (due Tuesday, September 4)
#2 (due Thursday, September 20)
#3 (due Tuesday, October 9)
#4 (due Thursday, October 25)
#5 (due Tuesday, November 13)
#6 (due Monday, December 3)
GRADES
Eduardo Mucciolo
2007-08-21
