Time Schedule:
Manjeri Anantram
E E 539
Seattle Campus
Lectures or discussions of topics of current interest in the field of solid-state electronics for advanced graduate students having adequate preparation in solid-state theory. Subject matter may vary according to the interests of students and faculty. Prerequisite: permission of instructor.
Class description
Quantum mechanics has entered main stream engineering over the last couple of decades. It is an useful language for students whose interests lie in areas such as nanomaterials, nanotechnology, photonics and quantum information. The purpose of this course is to introduce engineering graduate students to a working knowledge of basic quantum mechanics by a combination of theory and problem solving.
Topics
1) Schrodinger’s eqn a. Definition b. Interpretation c. Continuity equation for probability density d. Continuity of wave function and its first derivative e. Operators f. Uncertainity principle
2) Mathematical properties of wave function a. Completeness b. Orthonormality c. Bra-ket notation
4) Closed and Open systems a. Single Tunneling Barrier b. Double Barrier System (resonant tunneling) c. Separation of variables d. Nanowire e. Quantum Well f. Quantum Dot g. Hydrogen Atom h. Density of states of open and closed systems i. Time evolution of wave packets 3) Crystalline solid a. Unit cell b. Basis vectors c. Real space d. Reciprocal space via following examples i. 1D atom chain ii. 3D solid iii. Nanowire
4) Energy levels and wave function in a crystalline solid a. Bloch’s theorem b. Basic tight binding representation of a crystalline solid c. Examples (only single orbital per atom): i. Graphene ii. Carbon nanotube iii. Silicon Nanowire d. Density of States
5) Introduction to operator notation
6) Spins
7) Perturbation theory a. Calculation of transition rates b. Optical dipole matrix elements
Student learning goals
Learn to think quantum mechanically.
Developing problem solving ability.
Gain a basic understanding of quantum concepts in journal papers by end of course.
Learn quantum mechanics as applied to a subset of nanotechnology problems.
General method of instruction
Lectures
Problems Solving
Recommended preparation
None required except for basic differential equations and matrices.
Class assignments and grading
Problems in quantum mechanics, problem solving using math/computation. Discussion amongst students and with instructor is okay.
Will be announced in the first week of class.
