Thermodynamic properties and the confinement frequency for Second Pὃschl-Teller potential

The study of thermodynamic properties for different potentials as a function of temperature and maximum quantum state have been widely reported. In the present study, the authors examined the effect of the total confinement frequency (which is a combination of a confinement frequency ω0 and cyclotron frequency ωc) on some thermodynamic properties such as the vibrational enthalpy, the vibrational Gibbs free energy and the vibrational entropy. The energy level of the Second Pὃschl-Teller potential model is obtained using supersymmetric approach and shape invariance formalism. Then, the vibrational partition function is calculated from the energy level of the Second Pὃschl-Teller potential model using the Poisson summation formula. The vibrational thermodynamic properties are calculated from the partition function and its derivative. The result shows that the presence of the total confinement frequency lowers the vibrational enthalpy and entropy but reduces the negativity of the Gibbs free energy. The result also showcases that the magnetic field which is the main term in the cyclotron frequency has less decreasing effect on the enthalpy and entropy compared to the frequency as part of the total confinement frequency.