Flat minimal quantizations of Stackel systems and quantum separability
arXiv:1401.0434 · doi:10.1016/j.aop.2014.08.015
Abstract
In this paper, we consider the problem of quantization of classical Stäckel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of Stäckel transform, all considered systems are expressed by flat coordinates of related Euclidean configuration space. Then, the so-called flat minimal quantization procedure is applied in order to construct an appropriate Hermitian operator in the respective Hilbert space. Finally, we distinguish a class of Stäckel systems which remains separable after any of admissible flat minimal quantizations.
arXiv comment12 pages
References in corpus (9)
- Separation of Variables. New Trends.
- Classical and Quantum Integrable Systems in $\wt{\gr{gl}}(2)^{+*}$ and Separation of Variables
- Quantum integrability of quadratic Killing tensors
- Generalized Stäckel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems
- Natural coordinates for a class of Benenti systems
- Bi-Hamiltonian representation of Stäckel systems
- On reciprocal equivalence of Stäckel systems
- Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure
- Integrable quantum Stäckel systems