We considered the thermodynamics in spaces with deformed commutation relations leading to the existence of minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat capacity for ideal gas and harmonic oscillators using this method. The obtained results are in good agreement with the exact quantum ones. We also showed that the minimal length introduction reduces degrees of freedom of an arbitrary system in the high temperature limit significantly.

Spectrum and eigenfunctions in the momentum representation for 1D Coulomb-like potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that correction due to the deformation is proportional to square root of the deformation parameter. We obtain the same spectrum using Bohr-Sommerfeld quantization condition.

We construct a new class of non-Hermitian Hamiltonians with real spectra. The Hamiltonians possess one explicitly known eigenfunction.

We study the factorization of the P T symmetric Hamiltonian. The general expression for the superpotential corresponding to the P T symmetric potential is obtained and the explicit examples are presented.

Bohr-Sommerfeld quantization rule is generalized for the case of deformed commutation relation leading to minimal uncertainties in both coordinate and momentum operators. Correctness of the rule is verified by comparing obtained results with exact expressions for corresponding spectra.