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

UR - http://www.scopus.com/inward/record.url?scp=85019072085&partnerID=8YFLogxK

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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 -