Quantum 2025 – scientific programme

Parts | Days | Selection | Search | Updates | Downloads | Help

MON: Monday Contributed Sessions

MON 19: Foundational / Mathematical Aspects – Quantum Optics and Quantum Information

MON 19.8: Talk

Monday, September 8, 2025, 18:15–18:30, ZHG008

Lie-Algebraic quantum mechanics: exactly and quasi-exactly solvable models — •Mikhail Shifman — William Fine Theoretical Physics Institute, University of Minnesota, MN 55455, USA

Quantum mechanics is turning 100. It grew into a huge and omnipresent quantum science. Surprisingly, a class of spectral problems of the SchrÖdinger type unknown previously was discovered relatively recently and is still under development. The problems belonging to this class are distinguished by the fact that an (arbitrary) part of the eigenvalues and eigenfunctions can be found algebraically, but not the whole spectrum. The reason for the existence of such quasi-exactly-solvable problems is a hidden Lie-algebraic symmetry present in the Hamiltonian. For one-dimensional motion, this hidden symmetry is SL(2). The most elegant one-dimensional system in this class is the double well potential with x^6 highest term and one quantized parameter. Among N-body problems it is worth mentioning it is worth mentioning the Wolfs and elliptic Calogero models with two- and three-body interaction.