Approximation Methods

University of Colorado Boulder

Explore the world of quantum mechanics and learn commonly used approximation methods through the Approximation Methods course. Gain insight into time-independent perturbation theory and its applications, as well as the distinctions between non-degenerate and degenerate cases. Discover how to perform calculations using the variational method and obtain approximate solutions.

Throughout the course, you will delve into time-dependent perturbation theory, absorption, and stimulated emission processes, obtaining first- and second-order corrections to energies and wavefunctions, and transition rates. Additionally, you will be introduced to tight binding method and finite basis sets to solve various quantum mechanics problems.

By the end of the course, you will have the knowledge and skills to distinguish non-degenerate and degenerate cases and apply the appropriate methods, perform calculations using the time-independent perturbation theory, describe absorption and stimulated emission processes, and obtain approximate solutions using the variational method.

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Approximation Methods
Course Modules

This course consists of three modules that cover time-independent perturbation theory, time-dependent perturbation theory, and other approximation methods, such as the variational method, tight binding method, and finite basis sets.

Time-independent Perturbation Theory

Module 1 delves into time-independent perturbation theory, covering non-degenerate and degenerate cases, Stark effect, k-dot-p method, and fine structure. You will also explore physical constants, entering math expressions, and complete homework assignments.

Time-dependent Perturbation Theory

Module 2 focuses on time-dependent perturbation theory and includes topics like interaction picture, transition probabilities, Rabi oscillation, and homework assignments. You will gain a comprehensive understanding of time-dependent two-state problems and transition probability.

Other Approximation Methods

Module 3 introduces other approximation methods, such as the variational method, tight binding method, and finite basis set. You will gain insight into using finite basis and completing homework assignments to apply these approximation methods effectively.

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