ar X iv : h ep - t h / 99 11 01 4 v 1 3 N ov 1 99 9 Schrödinger quantum modes on the Taub - NUT background

The Schrödinger equation is investigated in the Euclidean TaubNUT geometry. The bound states are degenerate and an extra degeneracy is due to the conserved Runge-Lenz vector. The existence of the extra conserved quantities, quadratic in four-velocities implies the possibility of separating variables in two different coordinate systems. The eigenvalues and the eigenvectors are given in both cases in explicit, closed form. Pacs 04.62.+v E-mail: [email protected] E-mail: [email protected]