2016/07/22 by Hallnäs, Martin, Ruijsenaars, Simon · 4 citations
#Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1607.06672
In a previous paper we introduced and developed a recursive construction of joint eigenfunctions JN(a+,a-,b;x,y) for the Hamiltonians of the hyperbolic relativistic Calogero-Moser system with arbitrary particle number N. In this paper we focus on the cases N=2 and N=3, and establish a number of conjectured features of the corresponding joint eigenfunctions. More specifically, choosing a+,a- positive, we prove that J2(b;x,y) and J3(b;x,y) extend to globally meromorphic functions that satisfy various invariance properties as well as a duality relation. We also obtain detailed information on the asymptotic behavior of similarity transformed functions E2(b;x,y) and E3(b;x,y). In particular, we determine the dominant asymptotics for y1-y2→∞ and y1-y2,y2-y3→∞, resp., from which the conjectured factorized scattering can be read off.