Thermodynamical Properties and Superstatistic for Screened Modified Poschl-Teller Potential

The exact solution of the wave function in non-relativistic quantum mechanics can be studied using the Schrodinger equation. It has become a crucial part of the fundamental physical quantities in many physical sciences [1]. The non-relativistic spinless particles can be evaluated using the Schrodinger wave equation [2]. Different methods have been used to determine the approximate and exact solutions of the wave functions, such as asymptotic iteration method (AIM) [3], Laplace integral transform [4], Nikiforov–Uvarov method [5], improved AIM [6], factorization method [7], supersymmetry quantum mechanics (SUSY QM) [8], proper quantization rule and exact quantization rule [9]. The solution of the Schrodinger equation consists of the energy eigenvalue and eigenfunction. The wave function containing many of useful information in various fields such as atomic, nuclear, and high energy physics [10]. The limited research in this field makes an opportunity to explore and investigate more information of any molecule on the quantum scale. In this study, the Schrodinger equation under the influence of screened modified Poschl–Teller potential was solved using the SUSY QM method. In the case of one-dimensional Schrodinger equation to obtain energy level and wave function of shape invariant potentials, SUSY QM is a powerful tool. The relativistic energy spectrum is obtainable by using the idea of shape invariance and the wave functions are achieved by using lowering and raising SUSY operators [11]. The aim of this study was to obtain and analyze the energy levels, wave functions, thermodynamical properties, and superstatistics of the system. The Poschl–Teller potential is used to explain the physics of many systems which includes the excitons, quantum wires, and quantum dots [12]. The system is also influenced by the external field B together with Aharonov-Bohm field. The the Aharonov-Bohm field was used since it can perform better ability to remove degeneracy than magnetic [13]. By using appropriate variable transformation, the screened modified Poschl-Teller potential was reduced to general modified Rosen Morse-like potential. The energy spectra and the corresponding wave function were used to obtain the thermodynamical properties and Superstatistics of the system. Then the energy spectra were numerically calculated both for with and without Screened potential term. The result shows that by varying the parameters, (in this case the parameters are quantum number, potential height in the model, the potential width, and the screened parameter), the energy level changes and shift to lower or higher energies. Partition function was calculated for both with and without Screened parameters while the superstatistics partition function was calculated for the case without screened parameter. Other thermodynamics properties such as Helmholtz free energy, entropy, internal energy, and specific heat also could be evaluated using the partition function. The thermodynamical properties have also been evaluated before for the harmonic oscillator plus an inverse square term [7], shifted Deng–Fan potential [14], modified Rosen–Morse potential [15], and ordinary Poschl–Teller potential [12] which differs from the screened Poschl–Teller-type potential to be used in this study. These properties are the key to analyze the characteristic features of a system or particle. The ground state and some excited stated of the wave function equation were obtained in this work.