Explicit normalized eigenfunctions, interbasis expansions, and Euclidean-plane contraction limits are derived for the semi-circular, elliptic, and hyperbolic parabolic coordinate systems on the two-sheeted hyperboloid.
Reviewing the Helmholtz Equation on Euclidean Plane and Interbasis Expansions
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abstract
In the present paper we revisit the Helmholtz equation on the Euclidean plane and make some remarks on normalization constants and completeness of wave function sets. The coefficients of interbasis expansions are also reconsidered.
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Lie Algebra Contractions and Interbasis Expansions on Two-Dimensional Hyperboloid IIB. Non-Subgroup Basis
Explicit normalized eigenfunctions, interbasis expansions, and Euclidean-plane contraction limits are derived for the semi-circular, elliptic, and hyperbolic parabolic coordinate systems on the two-sheeted hyperboloid.