Superintegrability in classical and quantum mechanics
| advisor: | prof. Ing. Libor Šnobl, Ph.D. |
| e-mail: | show e-mail |
| type: | phd thesis |
| branch of study: | MI_MM |
| description: | Analytical investigation of dynamical systems both in classical and quantum mechanics often employs their integrals of motion. While the notion of an integrable system can be traced back to 19th century with original applications to celestial mechanics and played an indispensable role in the formulation of quantum mechanics in early 20th century, in the last few decades there has been a growing interest in systems with more integrals of motion than needed for integrability, the so-called superintegrable systems. Their structure often implies important properties like their exact solvability without the need to solve any differential equation or separability in several coordinate systems. The applicant can opt for one (or several) of the following topics of current interest: 1. Superintegrability with higher order integrals of motion, e.g. construction and classification of such systems, their simplification by means of canonical transformations. 2. Integrable and superintegrable systems in curved backgrounds, in particular with magnetic fields. 3. Polynomial algebras of integrals of motion and their applications to the investigation of quantum superintegrable systems, e.g. determination of energy spectra. |
| note: | Universidad Complutense de Madrid 3 months, geometrical aspects of separability and (super)integrability Co-supervisor: Prof. Piergiulio Tempesta, Universidad Complutense de Madrid, Department of Física Teórica |
| last update: | 20.04.2026 09:35:19 |
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