Approximate Methods in Quantum Mechanics (Englisch)

Abstract However light and elegant the mathematical apparatus of quantum mechanics appears, we can solve exactly only very few physically interesting problems with it. Therefore, we need to opt for appropriate approximations when facing the remaining vast majority of quantum-mechanical problems. In this chapter, we will introduce two basic approaches—the variational and perturbation method. Naturally, many other exist (for example the semi-classical approximations). However, those usually focus on a specific class of problems, while we can employ the variational and perturbative methods when facing almost any problem. We will illustrate both methods on the simplest problem one cannot solve analytically—the anharmonic oscillator.