Physics – Mathematical Physics
Scientific paper
2010-10-04
SIGMA 6 (2010), 097, 10 pages
Physics
Mathematical Physics
Proceedings of the Workshop Supersymmetric Quantum Mechanics and Spectral Design 2010, July 18 - July 30, Benasque, Spain
Scientific paper
10.3842/SIGMA.2010.097
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.
Ragnisco Orlando
Riglioni Danilo
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