Schrödinger quantum modes on the Taub-NUT background

Abstract

The Schrödinger 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.

16 pages, latex, no figures

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• Entropy of A Scalar Field In (3 + 1)-dimensional Taub-NUT Space-Time
• Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space
• The induced representation of the isometry group of the Euclidean Taub-NUT space and new spherical harmonics
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• Separation of Dirac equation in the 3+1 dimensional constant curvature black hole background and its solution
• Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems
• A note on Klein-Gordon equation in a generalized Kaluza-Klein monopole background