Uma solução algébrica para a parte radial do átomo de hidrogênio

Abstract

Here we find the bound states of the non-relativistic hydrogen atom using an operator method. The method adds the phase of a state and its associated operator to the set of variables of the system. The set of operators is found to form a closed set of commutation relations thus comprising an operator Lie algebra. From these relations, the energy spectrum and bounded radial eigenfunctions are calculated. The approach used is analogous to the one employed to compute the angular momentum spectrum and eigenfunctions but with operators satisfying an (1,1) Lie algebra instead of (2). The same operator algebra and minor modifications can be applied to solve the Dirac relativistic hydrogen atom.