Course Overview

Topics Included: Wave mechanics, Schroedinger equation, operators, harmonic oscillator, identical particles, atomic fine structure, approximation methods and applications.

Textbook: Quantum Mechanics: A Paradigms Approach—-a textbook that follows the paradigms approach. The chapters that are relevant to the Quantum Capstone course are:

9. One-dimensional Harmonic Oscillator

10. Time-Independent Perturbation Theory

11. Hyperfine Structure and the Addition of Angular Momentum

12. Perturbation of Hydrogen

13. Identical Particles

14. Time-Dependent Perturbation Theory

Sample Syllabus

Activities Included

Janet (2014). As I teach angular momentum this year, I find that the students may be better served by a different notation for coupled and uncoupled states.

I propose a subscript “c” or “u” on the kets to distinguish and the use of ALL FOUR quantum numbers in both the coupled and uncoupled bases. Such usage would reinforce that the particular state is an eigenstate of a particular set of operators.

At present, we distinguish between the two bases by dropping the individual angular momentum quantum numbers from the coupled basis, so that “2 quantum numbers” means coupled basis and “4 quantum numbers” means uncoupled basis. This efficiency is too advanced for novices, I think.

For example, we would use the following:

${{\left| \ell {{m}_{\ell}}s{{m}_{s}} \right\rangle }_{u}}$

${{\left| J{{m}_{J}}\ell s \right\rangle }_{c}}$

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