New ladder operators for the monopole harmonics

Abstract

Using the ladder operators shifting the index m of the associated Jacobi functions, for a given n, the monopole harmonics and their corresponding angular momentum operators are, respectively, extracted as the irreducible representation space and generators of su(2) Lie algebra. The indices n and m play the role of principal and azimuthal quantum numbers. By introducing the ladder operators shifting the index n of the same associated Jacobi functions, we also get a new type of the raising and lowering relations which are realized by the operators shifting only the index n of the monopole harmonics. Moreover, other symmetries, including the transformation of the irreducible representation spaces into each other, are derived based on the operators that shift the indices n and m of the monopole harmonics simultaneously and agreeably as well as simultaneously and inversely. Our results are reduced to spherical harmonics by eliminating magnetic charge of the monopole.