** 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

** Keywords: **