The Exactness of Supersymmetric Semiclassical Quantization

Semiclassical methods such as the WKB approximation can be used to obtain approximate solutions in quantum mechanics. In the context of supersymmetric quantum mechanics (SUSYQM), a supersymmetry-based version of the WKB method applies, known as the SWKB method. For a class of superpotentials known as conventional superpotentials, the SWKB method had been shown on a case-by-case basis to yield exact, rather than approximate solutions. We show that SWKB must be exact for all conventional superpotentials due to their required form arising from additive shape invariance. This exactness applies in both the broken and unbroken phases.