Course
Objective: This course will introduce the students
to the basic concepts and postulates of quantum mechanics. Examples will
include simple systems such as particle in an infinite and finite well, 1D and 2D
harmonic oscillator and tunneling. Numerous approximation techniques, such as
WKB method, time-dependent and time-independent perturbation theory, variational methods and numerical solution methods of the
1D Schrödinger equation, will be presented. In the
later, various ways of discretization of the 1D
Schrödinger equation for spatially varying effective
mass will be explained. Students will also be introduced to several methods for
solving the 1D eigenvalue problem (time-independent
Schrödinger equation), including shooting method, Lanczos
algorithm, etc.
Prerequisites: ECE 352 and EEE340, or an approval
by the instructor.
Instructor: Dr.
Dragica Vasileska (ERC565;
phone: 965-6651, e-mail:
vasilesk@imap2.asu.edu)
Text: D.K. Ferry,
Quantum Mechanics, 1987.
Course
Description: Waves versus particles, wave
packets, Schrödinger wave equation, interpretation of the wavefunction,
problems in one dimension, principles of wave mechanics, tunneling, angular
momentum, hydrogen atom, perturbation theory, numerical solution methods of the
1D Schrödinger equation.
Topics
Covered:
·
Introductory:
Why quantum physics?
·
Into
the microworld: Duality principle. Waves versus
particles.
·
The
state function and its interpretation.
·
Wave
packets in one dimension.
·
Observables
in quantum physics.
·
A
quantum equation of motion: The Schrödinger equation.
·
Tunneling
phenomena: Single barrier and double barrier case.
·
The
1D harmonic oscillator.
·
Basis
functions, operators and quantum dynamics: The importance of being Hermitian. Commuting and non-commuting operators.
·
Stationary
perturbation theory.
·
Time-dependent
perturbation theory.
·
Motion
in centrally symmetric potentials: 2D harmonic oscillator. The hydrogen atom.
·
Electrons
and anti-symmetry. Introduction of spin.
Grading:
2 Semester exams 40%
Homework (including computer work) 30%
Final exam 30%