Schr\"odinger quantum modes on the Taub-NUT background

TL;DR

This paper analyzes the Schr"odinger equation in Euclidean Taub-NUT geometry, revealing degenerate bound states and conserved quantities that enable variable separation, with explicit solutions provided.

Contribution

It provides explicit solutions for the Schr"odinger equation in Taub-NUT space, highlighting conserved quantities and degeneracies not previously detailed.

Findings

Bound states are degenerate due to conserved Runge-Lenz vector.

Extra conserved quantities allow separation of variables in two coordinate systems.

Eigenvalues and eigenvectors are explicitly derived in closed form.

Abstract

The Schr\"odinger equation is investigated in the Euclidean Taub-NUT 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.