Approximate analytical solutions to relativistic and nonrelativistic Pöschl–Teller potential with its thermodynamic properties

Abstract

We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrödinger equation in the presence of Pöschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of spin and pseudospin (p-spin) symmetries. We show that in the nonrelativistic limits, the solution of Dirac system converges to that of Schrödinger system. Rotational-Vibrational energy eigenvalues of some diatomic molecules are calculated. Some special cases of interest are studied such as S-wave case, reflectionless-type potential and symmetric hyperbolic PT potential. Furthermore, we present a high temperature partition function in order to study the behavior of the thermodynamic functions such as the vibrational mean energy U , specific heat C, free energy F and entropy S.

Spectroscopic study of some diatomic molecules via the proper quantization rule

“…[27], [29] and [31] and the conversion factors used are taken from NIST database [32]: 1cm −1 = 1.239841930eV,hc = 1973.29eVÅ and 1amu = 931.494061Mev/c 2 . In Table 2, we test the accuracy of the method utilized in this study by finding the energy spectra of H 2 and CO diatomic molecules.…”

Thermodynamic properties of diatomic molecule systems under SO(2,1)‐anharmonic Eckart potential

“…To verify the energetic behavior of molecules, we have compared some of the most important thermodynamic functions in analogy with other authors . We calculated the Morse potential and the EP parameters.…”

Non‐relativistic Eigen spectra with q‐deformed physical potentials by using the SUSY approach

“…The imaginary error function is an entire function defined by Erfi.x/ D iErf .ix/, and this function is implemented in mathematica as ErfiOEx, where erf denotes the error function is a special function of sigmoid shape, which occurs in probability, statistics, and partial differential equations. In mathematics, the error function can be denoted as [41,42] Erf .x/ D 2 ıp R x 0 e t 2 dt. Other thermodynamic properties of the system can be easily obtained from partition function.…”

“…In Eq. (30), the Dowson function or Dowson integral can be denoted as [41,42] F.x/ D e x 2 R x 0 e y 2 dy D p ı 2 e x 2 erfi.x/. Thus, the Dowson's integral is implemented in mathematica as DowsonFOEx.…”