Physics – Quantum Physics
Scientific paper
2011-02-27
Ann.Phys.326:2053-2073,2011
Physics
Quantum Physics
26 pages, 5 figures
Scientific paper
10.1016/j.aop.2011.03.002
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent kinetic energy, three different quantization prescriptions are worked out by imposing that the maximal superintegrability of the system has to be preserved after quantization. The relationships among these three Schroedinger problems are described in detail through appropriate similarity transformations. These three approaches are used to illustrate different features of the quantization problem on N-dimensional curved spaces or, alternatively, of position-dependent mass quantum Hamiltonians. This quantum oscillator is, to the best of our knowledge, the first example of a maximally superintegrable quantum system on an N-dimensional space with nonconstant curvature.
Ballesteros Angel
Enciso Alberto
Herranz Francisco J.
Ragnisco Orlando
Riglioni Danilo
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