A maximally superintegrable deformation of the N-dimensional quantum Kepler_Coulomb system

21st International Conference on Integrable Systems and Quantum Symmetries

Ballesteros, A.^1 ; Enciso, A.^2 ; Herranz, F.J.^1 ; Ragnisco, O.^3 ; Riglioni, D.^4

Departamento de Física, Universidad de Burgos, E-09001 Burgos, Spain^1

Instituto de Ciencias Matemáticas, CSIC, E-28049 Madrid, Spain^2

Dipartimento di Fisica, Università di Roma Tre, Sezione di Roma Tre, Via Vasca Navale 84, I-00146 Roma, Italy^3

Centre de Recherches Mathématiques, Université de Montréal, 2920 Chemin de la tour, Montreal H3T 1J4, Canada^4

关键词: Coulomb systems;    Coupling constants;    Deformation parameter;    Hamiltonian systems;    Positive value;    Quantum Hamiltonians;    Riemannian spaces;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012008/pdf
DOI  :  10.1088/1742-6596/474/1/012008

来源: IOP

【 摘 要 】

The N-dimensional quantum Hamiltonian Hˆ = -2|q|/ 2(η+|q|) dtri;2- k/η+|q| is shown to be exactly solvable for any real positive value of the parameter η. Algebraically, this Hamiltonian system can be regarded as a new maximally superintegrable η-deformation of the N-dimensional Kepler-Coulomb Hamiltonian while, from a geometric viewpoint, this superintegrable Hamiltonian can be interpreted as a system on an N-dimensional Riemannian space with nonconstant curvature. The eigenvalues and eigenfunctions of the model are explicitly obtained, and the spectrum presents a hydrogen-like shape for positive values of the deformation parameter η and of the coupling constant k.