TY - JOUR
T1 - Three-body problem in 3D space
T2 - Ground state, (quasi)-exact-solvability
AU - Turbiner, Alexander V.
AU - Miller, Willard
AU - Escobar-Ruiz, Adrian M.
N1 - Publisher Copyright:
© 2017 IOP Publishing Ltd.
PY - 2017/5/2
Y1 - 2017/5/2
N2 - We study aspects of the quantum and classical dynamics of a 3-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories in the classical case are of this type. The quantum (and classical) 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 three-body generalized harmonic oscillator-type potential as well as a quasi-exactly-solvable three-body sextic polynomial type potential; both models have an extra integral.
AB - We study aspects of the quantum and classical dynamics of a 3-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories in the classical case are of this type. The quantum (and classical) 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 three-body generalized harmonic oscillator-type potential as well as a quasi-exactly-solvable three-body sextic polynomial type potential; both models have an extra integral.
KW - (quasi)-exact-solvability
KW - hidden algebra
KW - three-body problem
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U2 - 10.1088/1751-8121/aa6cc2
DO - 10.1088/1751-8121/aa6cc2
M3 - Article
AN - SCOPUS:85019072085
SN - 1751-8113
VL - 50
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 21
M1 - 215201
ER -