Application of the SUSY semiclassical quantisation rule to non-solvable potentials

General features of the SUSY semiclassical quantisation rule including higher-order corrections are discussed in relation to non-solvable potentials. The pairing between the levels of the SUSY partner Hamiltonians is shown to hold in every order of the approximation up to the fifth. This result appears to be true in all orders. A class of non-solvable superpotentials phi =x2N+1/2N+1 is studied in some detail and numerical results for the case N=1 are presented.