Algebraic Perturbation Theory for Hydrogen Atom in Weak Electric Fields

An algorithm for symbolic calculation of eigenvalues and eigenfunctions of a hydrogen atom in weak electric fields is suggested. A perturbation theory scheme is constructed that is based on an irreducible infinite-dimensional representation of algebra so(4, 2) of the group of dynamical symmetry for the hydrogen atom 1]. The scheme implementation does not rely on the assumption that the independent variables of the perturbation operator can be separated, and fractional powers of parabolic quantum numbers are not used in the recurrent relations determining the operation of algebra generators on the corresponding basis of the irreducible representation 2]. A seventh-order correction to the energy spectrum of the hydrogen atom in a uniform electric field is given. The algorithm suggested is implemented in REDUCE 3.6 4].