Generalized Lame functions. I. The elliptic case

We present and study a class of functions associated with the two-particle quantum relativistic Calogero-Moser system with elliptic interactions. The functions may be viewed as joint eigenfunctions of two independent commutin g analytic difference operators, one of which is the defining quantum dynam ics; The second one is obtained by interchanging the step size and the imag inary period. The functions depend on parameters that are dense in the natu ral parameter domain. In essence, they consist of products of Weierstrass s igma-functions and plane waves. The zeros of the sigma-functions satisfy a constraint system encoding both Schrodinger equations at once. (C) 1999 Ame rican Institute of Physics. [S0022-2488(99)02402-0].