Event
Adrian Escobar, UNAM et CRM
Tuesday, January 17, 2017 15:30to16:30
Room 4336, Pavillon Andr茅-Aisenstadt, 2920, Chemin de la tour, 5th floor, Montreal, QC, H3T 1J4, CA
Three-body problem in 3D space: ground state, (quasi)-exact-solvability.
In this talk we discuss aspects of the quantum 3-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions which are functions of mutual distances only. The quantum system for which these states are eigenstates is found and its Hamiltonian is constructed. It corresponds to a three-dimensional quantum particle moving in a curved space with special metric. The kinetic energy of the system has a hidden sl(4,R) Lie (Poisson) algebra structure, alternatively, the hidden algebra $h^{(3)}$ typical for the $H_3$ Calogero model. We find an exactly solvable 3-body generalized harmonic oscillator-type potential as well as a quasi-exactly-solvable 3-body sextic polynomial potential.