## 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 *L _{z}*. Angular momentum in three dimensions. Eigenvalues of

*L*e

^{2}*L*

*. Central potentials. Spin.*

_{z}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