Quasi-doubly periodic solutions to a generalized Lame equation

Details Quasi-doubly periodic solutions to a generalized Lame equation Quasi-doubly periodic solutions to a generalized Lame equation

2007-06-05

arxiv.org/abs/0706.0612v1

Physics

Mathematical Physics

15 pages,1 table, accepted for publication in Journal of Physics A

Scientific paper

10.1088/1751-8113/40/27/016

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.

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