Statistical Properties of the 1D Space Fractional Klein-Gordon Oscillator

In this paper, we investigate the quantum fractional of the one-dimensional Klein-Gordon oscillator. By using a semiclassical approximation, the energy eigenvalues have been determined for oscillators. The obtained results show a remarkable influence of the fractional parameter alpha on the energy eigenvalues. By considering a unique energy spectrum, we present a simple numerical computation of the thermal properties of a defined energy spectrum of a system. The Euler-Maclaurin formula has been used to calculate the partition function and therefore the associated thermodynamics quantities. Besides this, we also calculate the eigenfunctions of our problem. The influence of the parameter alpha on these functions as well as the probability of density has been tested.