REQUIRED TEXTS: A. Yariv, Quantum Electronics , Wiley & Sons, 3 rd edition (1989)
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.
- 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.