Approximation Methods

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  • Time-independent Perturbation Theory
    • In this module we will introduce the course on approximation methods commonly used in quantum mechanics and then discuss time-independent perturbation theory. We will first discuss non-degenerate perturbation theory and derive useful formulas for the first- and second-order corrections. We will then discuss degenerate perturbation theory. We will also discuss specific examples where the various perturbation methods are used - Stark effect, fine structure and Zeeman effect.
  • Time-dependent Perturbation Theory
    • In this module, we will introduce interaction picture and derive time evolution equations. After discussing a simple but illuminating example of two-state system, we develop time-dependent perturbation theory and discuss the probability of transitions between quantum states induced by external perturbation.
  • Other Approximation Methods
    • This module covers several non-perturbative approximation methods. They are the tight binding method, variational method and the use of finite basis set.