The eigenvalue equation on the Eguchi-Hanson space

Details The eigenvalue equation on the Eguchi-Hanson space The eigenvalue equation on the Eguchi-Hanson space

2002-10-06

arxiv.org/abs/math/0210081v2

J.Math.Phys. 44 (2003) 4308-4343

Mathematics

Differential Geometry

29 pages, 32 figures

Scientific paper

10.1063/1.1579548

We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation with Ince symbol [0,2,1_2]. We construct approximations for the eigenfunctions and their asymptotic scattering phases with the help of the Liouville-Green approximation (WKB). Furthermore, for specific discrete eigenvalues obtained by a continued T-fraction we construct the solution by the Frobenius method and determine its scattering phase by a monodromy computation.

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