Symbolic Algorithms of Algebraic Perturbation Theory: Hydrogen Atom in the Field of Distant Charge

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We present symbolic algorithms implemented in REDUCE 3.6 for evaluation of eigenvalues and eigenfunctions of a hydrogen atom in the field of a distant point charge. These solutions are presented as perturbation series by a small parameter. This parameter is the inverse value of the separation between the distant point charge and the hydrogen like atom nucleus. Algebraic perturbation theory schemes are built up using the irreducible representations of the dynamical symmetry algebra so(4,2). The representations are connected by the tilting transformations with wave functions of the discrete spectrum of the hydrogen atom in an arbitrary bound state characterized by a set of parabolic or spherical quantum numbers. Such a construction is based on a reduction of the unperturbed Hamiltonian and polynomial perturbation operators via generators of the algebra. The efficiency of the proposed perturbation scheme and symbolic algorithm is demonstrated by calculating the coefficients of the high order perturbation series via the parabolic quantum numbers.