CRC Press eBooks

Approximation Methods

A. C. Sharma

Published Jun 18, 2021• 0 citations

Abstract

Perturbation theory for non-degenerate and degenerate systems, variational methods, and WKB approximation are covered in this chapter. First, second, and kth order corrections to energy and wave function ket of non-degenerate states, energy eigenvalues, and wave functions kets of anharmonic oscillator, first-order perturbation theory for degenerate states and linear stark effect are written under perturbation theory. Second part of the chapter includes the variational methods for computation of the energy for ground state of helium atom, Rayleigh-Ritz variational method and its application to hydrogen molecule ion, calculation of energy of excited states, and its application to 1D harmonic oscillator. The topics which are covered under WKB approximation are the classical and non-classical regions of particle motion, alternative derivation of WKB formulae, connecting formulae, and quantum condition for bound state. The kth order corrections to energy and wave function kets for non-degenerate perturbation theory, treatment of WKB approximation from two different approaches and the detailed derivation of connecting formulae, application of variational method to compute energy for excited states are topics which are not generally found in existing text books on quantum mechanics. A good number of solved examples illustrating the importance of approximation methods in contemporary fields are added at the end of chapter.

DOI: 10.1201/9781003154457-7

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