PHYSICS 5606 – Quantum Mechanics I

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.


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.


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)


Extra Assignment (due Thursday, November 16, at 5pm)

Eduardo Mucciolo 2006-11-14