## EECS 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 & Sons, 3 rd edition (1989)

**REFERENCE TEXTS: **None.

**COURSE INSTRUCTOR:** **Prof. Selim Shahriar**

**COURSE DIRECTOR: Prof. 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:

- 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.
- 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.
- 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.
- Understand the origin of the matrix formulation of Q.M., and how it relates to the operator formulation.
- Understand how peturbation theory can be used to calculate interaction strengths; understand in particular the origin and significance of Fermi's Golden Rule.
- 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.
- 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.
- Understand the parallel between propagation of light rays in graded index media, and the Schrodinger equation for a particle in a potential well.
- 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.
- Understand how the density matrix formalism can be used to study photon statistics, and how Gaussian or Poisson statistics are obtained under different circumstances.