Approximation Methods of Quantum Mechanics

Abstract

In Chaps. 1–3 we have focused on solving eigenvalue equations with respect to a particle confined within a one-dimensional potential well or a harmonic oscillator along with an electron of a hydrogen-like atom. In each example we obtained exact analytical solutions with the quantum-mechanical states and corresponding eigenvalues (energy, angular momentum, etc.). In most cases of quantum-mechanical problems, however, we are not able to get such analytical solutions or accurately determine the corresponding eigenvalues. Under these circumstances, we need appropriate approximation methods of those problems. Among those methods, the perturbation method and variational method are widely used.