Abstract
If a wave function is written in polar form it becomes possible to write the Schr\"odinger equation of nonrelativistic quantum mechanics in a form analogous to the classical Hamilton-Jacobi equation with an extra term known as the quantum potential. Time-dependent supersymmetry is a procedure for finding new solutions of the Schr\"odinger equation if one solution is known. In this paper a time-dependent supersymmetry transformation is applied to a wave function in this polar form and it is shown that the classical potential plus the quantum potential is a conserved quantity under this transformation under certain circumstances. This leads to a modification of our view of the role of the quantum potential and also to a deeper appreciation of the function of a supersymmetry transformation.
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