Courses Detail Information

ECE6203J – Applied Quantum Mechanics I

Instructors:

Credits: 3 credits

Pre-requisites: Physics II (or Honors Physics II); Applied Calculus IV (or Honors Mathematics IV)

Description:

The course introduces the formalism of quantum mechanics in a standard approach based on the
concept of the wave function and its probabilistic interpretation. The postulates of quantum
mechanics are formulated and applied to discuss one- and three-dimensional problems, with an
emphasis on those relevant to applications in atomic and solid state physics/optics. A range of
approximate methods of quantum mechanics is introduced and illustrated

Course Topics:

Introduction: experiments and theories – towards quantum mechanics (black
body radiation; photoelectric effect; Compton scattering; Bohr’s model of the
hydrogen atom; de Broglie hypothesis and matter waves; Young’s double-slit
experiment);
Postulates of quantum mechanics (wave function and its interpretation; time
evolution and the Schrödinger equation; observables and Hermitian operators;
Dirac’s notation; stationary Schrödinger equation; quantum-mechanical
measurement);
Schrödinger equation in the position representation – bound states:
analytically solvable models in one dimension (infinite quantum well;
harmonic oscillator);
Schrödinger equation in the position representation – bound states
(continued): other one-dimensional models (finite quantum well; double
quantum well);
Schrödinger equation in the position representation – unbound states in one
dimension (free particle; quantum wave packets; scattering; quantum
tunneling);
Schrödinger-Robertson uncertainty principle (special case: Heisenberg
uncertainty principle) and its consequences; complete sets of observables;
chapter 5
three dimensional problems (bound states in a 3D quantum well; harmonic
oscillator) and the hydrogen atom;
hree dimensional problems (bound states in a 3D quantum well; harmonic
oscillator) and the hydrogen atom;
Spin and total angular momentum; introduction to quantum mechanics of
multi-particle systems; bosons and fermions;
Approximate methods in quantum mechanics I: perturbation theory for
stationary states
Approximate methods in quantum mechanics II: Time-dependent
perturbations and Fermi’s golden rule; interaction of light with matter and
selection rules; Rayleigh–Ritz variational rule;
Introduction to solid state physics: Krönig-Penney model of a one
dimensional crystal; band structure of solids; Fermi gas (time permitting);