Path Integral Over Single-Sheeted Hyperboloid and Related Potentials

Authors: Hacı AHMEDOV

Abstract: Path integral over single-sheeted hyperboloid is evaluated. To relate the obtained propagator to quantum system we choose the part of it which is invariant with respect to reflection. This part corresponds to the propagator of the free particle motion on the invariant subspace of M- Imaginary Lobachevsky space. The wave functions and spectra for the quantum systems with potentials -\frac{\nu^{2}+\frac{1}{4}}{\sin h^{2}x} and -\frac{\nu^{2}+\frac{1}{4}}{\sin^{2}x} is given. Note that these potentials are not the special case of Rosen-Morse or the modified P\"{o}schl-Teller ones