COURSE TITLE: ECE 404 Quantum Electronics

CATALOG DESCRIPTION: Review of quantum mechanics. Harmonic oscillator. Perturbation theory. Phonons and photons. Interaction of radiation and atomic systems. Einstein coefficients. Laser oscillation. Laser photon statistics.

REQUIRED TEXTS: A. Yariv, Quantum Electronics, Wiley, New York, 1989 (3^rd edition).

REFERENCE TEXTS: None.

COURSE DIRECTOR: Prem Kumar

COURSE GOALS: To review the basic principles of quantum mechanics, and study specific applications, with particular emphasis on topics of interest to graduate students in electrical engineering. Topics include: axioms of quantum mechanics; operators; wavefunction; Schrodinger equation; the hydrogen atom; the harmonic oscillator, creation and annihilation operators; matrix formulation; perturbation theory; lattice vibrations and phonons; electromagnetic fields and their quantization, photons; interaction of radiation and atomic systems; spontaneous and induced transitions; Einstein coefficients; photon statistics.

PREREQUISITES BY TOPIC: Graduate standing in Electrical and Computer Engineering.

DETAILED COURSE TOPICS:

Week 1: Review of Quantum Mechanics

Week 2-3: Hydrogen atom; harmonic oscillator, coherent states

Week 4: WKB approximation and “Old Q. M.”

Week 5: Matrix formulation; perturbation theory; Fermi’s Golden Rule

Week 6: Lattice vibrations and their quantization; phonons

Week 7: Electromagnetic fields and their quantization: Slater modes; second quantization; photons

Week 8: Optical beams in lenslike media: Ray tracing; equation for quasi-plane waves

Week 9-10 Interaction of radiation and atomic systems: atomic susceptibility; atomic transitions; Einstein coefficients

COMPUTER USAGE: Use of Matlab, Mathematica, or equivalent.

GRADES:

Homework – 30%

Midterm exam – 30%

Final exam – 40%

COURSE OBJECTIVES: When a student completes this course, s/he should be able to:

1. Understand basic concepts of quantum mechanics, such as wave functions, uncertainty principle, etc., and their applicability to the description of electrical charges and electromagnetic fields.

2. Perform calculations of energy levels and wavefunctions for standard potential wells. In particular, become familiar with the properties of the harmonic oscillator, including creation and annihilation operators.

3. Understand the principles of the “Old Quantum Mechanics,” and be able to use the WKB method to gain considerable insight into the form of the wavefunctions in arbitrary potential wells.

4. Understand the origin of the matrix formulation of Q.M., and how it relates to the operator formulation.

5. Understand how peturbation theory can be used to calculate interaction strengths; understand in particular the origin and significance of Fermi’s Golden Rule.

6. Understand the dynamics of lattice vibrations from a classical standpoint; be able to make the transition to the Q.M. description, and their quantization. Understand the concept of phonons and their properties.

7. Understand the classical modes of resonance of the electromagnetic field, and make the transtion to the Q.M. description, and their quantization. Understand the concept of photons and their properties.

8. Understand the parallel between propagation of light rays in graded index media, and the Schrodinger equation for a particle in a potential well.

9. Understand the Q.M. treatment of the interaction between the electromagnetic field and an atom, and the origin of spontaneous and stimulated transitions; understand the Q.M. calculation of the Einstein coefficients, and its agreement with the semi-classical result.

10. Understand how the density matrix formalism can be used to study photon statistics, and how Gaussian or Poisson statistics are obtained under different circumstances.