21st International Conference on Integrable Systems and Quantum Symmetries | |
A maximally superintegrable deformation of the N-dimensional quantum Kepler_Coulomb system | |
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 |
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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.
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A maximally superintegrable deformation of the N-dimensional quantum Kepler_Coulomb system | 483KB | download |