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Quantum Mechanics with Basic Field Theory by Bipin R. Desai

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24 Approximation methods for bound states and scattering

Having looked at solutions that are obtained exactly or through perturbation theory, we now consider cases where we have to resort to some unique approximation schemes, both for scattering and for bound states. In relation to the bound states we introduce the WKB approximation, and the variational method. For scattering at high energies we introduce the eikonal approximation, which is closely allied to the WKB method.

24.1 WKB approximation

24.1.1 Introduction

 

We begin with the Schrödinger equation in one dimension,

images

which we write as

If V(x) is a constant, equal to V0, then in that ...

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