Supersymmetric Schrödinger operators: an alternative approach using pseudo-differential operators

An asymptotic method based on the calculus of pseudo-differential operators is used to derive the well-known relations between one-particle supersymmetric partner Hamiltonians. This alternative approach will be applied to one of the standard examples of supersymmetric quantum mechanics, where all the known analytical results will be reproduced. We also note a fundamental uncertainty relation between an operator and its formal left and right inverses.