LOCAL SYMMETRY ALGEBRA OF THE SCHRODINGER-EQUATION FOR THE HYDROGEN-ATOM

We completely describe all local symmetries (that is, differential ope rators of arbitrary finite orders) of the steady-state Schrodinger equ ation for the hydrogen atom. This description is based on the reductio n of the Schrodinger equation for an isotropic harmonic oscillator to the Schrodinger equation for the hydrogen atom, which generates the re duction of the corresponding symmetry algebras. We show that for an n- dimensional isotropic harmonic oscillator, all nontrivial local symmet ry operators belong to the enveloping algebra U(su(n, C)) of the algeb ra su(n, C). The basis of so(4, C) consists of rotation group generato rs and Runge-Lenz operators.