Fityo T. New exactly and quasi-exactly solvable quantum systems

Methods of constructing exactly and quasi-exactly solvable quantum mechanical problems are investigated. A general expression of superpotential leading to PT-symmetric Hamiltonian is obtained. A new class of non-Hermitian Hamiltonians with real spectra is constructed. Inverse method for construction of quasi-exactly solvable problems is generalized for the cases of multidimensional stationary Schroedinger equation and non-stationary one. A spectrum of one-dimensional Coulomb problem is found in the space with the minimal length. Semiclassical approximation is generalized to the case of one-dimensional space with deformed commutation relations. The results are used in the educational process, in scientific work. Application realm is the theory of one-particle quantum systems.