Fall 2006
Lecturer: Eduardo Mucciolo (office in MAP 416, ext 3-1882, e-address: mylastname at physics dot ucf dot edu
Schedule and Location: Mondays and Wednesdays, 04:30-5:45 pm, in the Math and Physics Building, room 306. Office hours: Mondays 02:00-04:00pm and Tuesdays 10:00am-12:00 pm.
Credit hours: 3 units.
Prerequisites: 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. Spin.
10) Addition of Angular Momentum: Simplified version. General version. Clebsch-Gordan coefficients. Irreducible tensor operators. Degeneracies.
Textbook: Principles of Quantum Mechanics, 2nd edition, by R. Shankar (Plenum Press, 1994).
Other useful books for this course are: Modern Quantum Mechanics, 2nd edition, by J. J. Sakurai (Addison-Wesley, 1994); Quantum Mechanics: Non-Relativistic Theory, 3rd edition, by E. M. Lifshitz and L. D. Landau (Butterworth-Heinemann, 1981).
Grading: Final grades will be based on homework (1/3), a mid-term (1/3), and a final 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 13 (Friday), in a location to be announced. The final exam has been schedule for December 04 (Monday), from 4:00-6:50 pm in MAP 306.
CALENDAR
PROBLEM SETS (pdf files)
#1 (due Tuesday, September 05)
#2 (due Thursday, September 21)
#3 (due Tuesday, October 10)
#4 (due Thursday, October 26)
#5 (due Tuesday, November 14)
#6 (due Thursday, November 30)
ADDITIONAL MATERIAL, ETC (pdf files)
Extra Assignment (due Thursday, November 16, at 5pm)
Eduardo Mucciolo 2006-11-14