The main object of the present paper is to investigate the Dirac equation (Dirac fermions) in presence of scalar and vector potential in a class of flat Gödel-type space-time called Som-Raychaudhuri space-time by using the methods quasi-exactly solvable (QES) differential equations and the Nikiforov Uvarov (NU) form. In addition, we evaluate the Einstein, and the Papapetrou.

In this paper, we find solutions for the Klein–Gordon equation in the presence of a Cornell potential under the influence of noninertial effects in the cosmic string space-time. Then, we study Klein–Gordon oscillator in the cosmic string space-time. In addition, we show that the presence of a Cornell potential causes the forming bound states for the Klein–Gordon equation in this kind of background.

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In this work, based on the generalized Dunkl derivative in quantum mechanics we study the one-dimensional Schrödinger equation with a harmonic oscillator potential and obtain the energy eigenvalues. The principal thermodynamical properties including the Helmholtz free energy, mean energy and entropy are carried out. The effects of the Dunkl parameters on the thermodynamical quantities for even parity are discussed. The case of the odd parity can be easily obtained by substitution of the b → −b and γ → −γ. All results in the limit case are reduced to ordinary statistical mechanics.

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