520.457, Basics of Quantum and Wave Mechanics for Engineers

Catalog Data:
Topics include brief review of classical mechanics of particles and waves; "derivation" of Schroedinger equation; the quantum theory of simplest systems, in particular atoms and engineered quantum wells, the interaction of radiation and atomic systems, and examples of application of the quantum theory to lasers and solid-state devices.

Credit hours for each Part: 3

Prerequisite: general intro-physics; math: differential eqns 171.101-102; 520:219-220; 11:302
Instructor: Prof. Alexander Kaplan ECE; Barton Hall, #304, ph 7018

Text: class notes handed out by instructor. See the table of contents for the first part
Supplemental recommended text: P. L. Hagelstein, S. D. Senturia, T. P. Orlando, Introductory Applied Quantum and Statistical Mechanics , Wiley, 2004; Also recommended: R. L. Libov, Introduction to Quantum Mechanics , Addison-Wesley, 1992; W. Greiner, Quantum Mechanics; Introduction , Springer, 1989.

Other recommended books for Part II: Amnon Yariv, Quantum Electronics , 3-rd edition, John Wiley, 1989 R. H. Bube, Electrons in solids , Acad. Press, 1988 D. E. Eastman, Atomic Physics of Lasers , Taylor & Francis, 1989


Goals:
The course is intended to expose undergrads and junior graduates to the basic principles of quantum physics and its application in engineering fields, such as lasers, solid state, etc. It is intended to be an introductory course to "Lasers", "Solid-state", "Quantum Electronics", "Nonlinear Optics", and "Electr. & Opt. Properties of Materials", and to cover the needs of most of departments in the School of Engineering.

Topics:

Part I

1. Intro: quantum mechanics in a nut-shell
2. classical mechanics of particles
3. classical mechanics of waves; EM waves
4. waves vs particles; the Schroedinger wave equation
5. QM operators, mean values and uncertainty relations
6. wavefunctions, eigenfunctions, eigenstates and energy levels
7. Time-dependent problems: expantion of QM-packet in a free space
8. "Philosophical" matters: measurements, wavefuntion collapse, etc.
9. quantum theory of particle motion in simplest 1-D potentials:
   harmonic oscillator, rectangular quantum well of infinite and finite depth, etc.
10. quantum mechanics of electrical circuits
11. Reflection, transmission and tunneling in 1D-scattering
12. quantum theory of hydrogen atom; 3-D wavefunctions and quantum numbers
13. course project: literature search and seminar-style presentation on recent QM applications and discoveries
14. review and final exam
    
    Part II (second semester)
    
15. Spin
16. transition from QM back to classical mechanics
17. the interaction of light with quantum system; radiative transitions, atomic susceptibilities, absorption and dispersion
18. Two-level model: a work-horse of quantum electronics
19. stimulated emission and basics of lasers
20. basics of nonlinear optics
21. brief review of "extreme" nonlinear optics
22. electrons in solids; free-electron model; photoemission; energy bands in crystal lattice
23. course project: literature search and seminar-style presentation on recent QM applications and discoveries
24. review and final exam