Path Integral Discussion for Smorodinsky-Winternitz Potentials: I. Two- and Three Dimensional Euclidean Space

1994/02/22 by C. Grosche, G. S. Pogosyan, A. N. Sissakian · 4 citations
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th

paper · pdf · doi:10.1002/prop.2190430602

published as Fortsch.Phys.43:453-521,1995 · LaTeX 60 pages, DESY 94-018

arxiv created 1994/02/22 · openalex publication_date 1995/01/01 · arxiv updated 2011/08/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave-functions.

Citations

• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels
• Significance of Electromagnetic Potentials in the Quantum Theory
• Construction of new integrable Hamiltonians in two degrees of freedom

Cited by

• Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions
• Harmonic Oscillator on the SO(2,2) Hyperboloid
• Kepler motion on single-sheet hyperboloid
• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles