Generators of the de Sitter Group for the Hydrogen Atom

Abstract

Explicit Hermitian operator functions of q and p are constructed for the generators of the de Sitter group $O(4, 1)$ on the bound-state wave functions for the hydrogen atom. This is done for each of the one-parameter family of irreducible unitary representations of $O(4, 1)$ in which the irreducible representations of the four-dimensional rotation group $O(4)$ correspond to the degeneracy subspaces of the bound-state energy levels. The commutation relations and the values of the invariants which label the representation of $O(4, 1)$ are verified by direct operator calculations.