Abstract
In this chapter we will consider a quasi-classical evaluation of the path-integral for the Witten model. In contrast to the usual semi-classical evaluation of the path integral, where one expands the action about the classical paths up to second order, we propose a modified approach by expanding the action about the quasi-classical paths. We arrive in the case of good SUSY at a quantization condition which has previously been suggested by Comtet, Bandrauk and Campbell [CoBaCa85]. For broken SUSY we find a modified form of this quantization condition [InJu93a]. A remarkable property of these two quasi-classical SUSY formulas is that they yield the exact discrete spectrum for all shape-invariant potentials. In combination with the usual WKB formula they are also useful for not shape-invariant (i.e. not exactly soluble) potentials.
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