A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum
arXiv:1010.0641 · doi:10.3842/SIGMA.2010.097
Abstract
A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetry. The high number of symmetries (both geometrical and dynamical) exhibited by the classical systems has a counterpart in the accidental degeneracy in the spectrum of the quantum systems. This family of quantum problem is completely solved with the techniques of the SUSYQM (supersymmetric quantum mechanics). We also analyze in detail the ordering problem arising in the quantization of the kinetic term of the classical Hamiltonian, stressing the link existing between two physically meaningful quantizations: the geometrical quantization and the position dependent mass quantization.
Proceedings of the Workshop Supersymmetric Quantum Mechanics and Spectral Design 2010, July 18 - July 30, Benasque, Spain
References in corpus (3)
Cited by in corpus (6)
- Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass
- Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
- Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform
- Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups
- Curvature as an integrable deformation
- Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 2. Systems with dilatation and shift symmetries