Supersymmetric Quantum Mechanics and Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>Expansions

Abstract

Supersymmetric quantum mechanics is formulated for spherically symmetric potentials in $N$ spatial dimensions. It is seen that the supersymmetric partner potential of a given potential can be effectively treated as being in $N+2$ dimensions. This fact is exploited in calculations using the shifted $\frac{1}{N}$ expansion. Also, the violation of the no-degeneracy theorem in one dimension by the Coulomb potential is seen as a consequence of this result.