We propose the exact
solution of the equation in separated variable which appears in the process of
constructing solutions to the quantum Calogero-Moser three-particle problem
with elliptic two-particle potential . This solution is found
for special values of coupling constants . It can be used for solving three-particle
Calogero-Moser problem under the appropriate boundary conditions.
References
[1]
Sutherland, B. (1971) Quantum Many-Body Problem in One Dimension: Ground State. Journal of Mathematical Physics, 12, 246-250. https://doi.org/10.1063/1.1665584
[2]
Sutherland, B. (1972) Exact Results for a Quantum Many-Body Problem in One Dimension II. Physical Review A, 5, 1372-1376. https://doi.org/10.1103/PhysRevA.5.1372
[3]
Olshanetsky, M.A. and Perelomov, A.M. (1983) Quantum Integrable Systems Related to Lie Algebras. Physics Reports, 94, 313-404. https://doi.org/10.1016/0370-1573(83)90018-2
[4]
Calogero, F. (1975) Exactly Solvable One-Dimensional Many-Body Problems. Lettere al Nuovo Cimento, 13, 411-416. https://doi.org/10.1007/BF02790495
[5]
Moser, J. (1975) Three Integrable Hamiltonian Systems Connected with Isospectral Deformations. Advances in Mathematics, 16, 197-220. https://doi.org/10.1016/0001-8708(75)90151-6
[6]
Whittaker, E.T. and Watson, G.N. (1927) A Course of Modern Analysis. University Press, Cambridge.
[7]
Dittrich, J. and Inozemtsev, V.I. (1993) On the Structure of Eigenvectors of Multidimensional Lamé Operator. Journal of Physics A: Mathematical and General, 26, L753-L756. https://doi.org/10.1088/0305-4470/26/16/008
[8]
Felder, G. and Varchenko, A. (1995) Integral Representation of Solutions of the Elliptic Knizhnik-Zamolodchikov-Bernard Equations. International Mathematics Research Notices, 5, 221-233. https://doi.org/10.1155/S1073792895000171
[9]
Komori, Y. and Takemura, K. (2002) The Perturbation of the Quantum Calogero-Moser-Sutherland System and Related Results. Communications in Mathematical Physics, 227, 93-118. https://doi.org/10.1007/s002200200622
[10]
Sklyanin, E.K. (1995) Separation of Variables: New Trends. Progress of Theoretical Physics Supplement, 118, 35-60. https://doi.org/10.1143/PTPS.118.35