Quasi-doubly periodic solutions to a generalized Lame equation

Abstract

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.

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

References in corpus (2)

• Kink scaling functions in 2D non--integrable quantum field theories
• Fuchsian equation, Hermite-Krichever Ansatz and Painlevé equation

Cited by in corpus (1)

• On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain