Bound-state solutions and thermal properties of the modified Tietz–Hua potential

Abstract

An approximate solutions of the radial Schrödinger equation was obtained under a modified Tietz–Hua potential via supersymmetric approach. The effect of the modified parameter and optimization parameter respectively on energy eigenvalues were graphically and numerically examined. The comparison of the energy eigenvalues of modified Tietz–Hua potential and the actual Tietz–Hua potential were examined. The ro-vibrational energy of four molecules were also presented numerically. The thermal properties of the modified Tietz–Hua potential were calculated and the effect of temperature on each of the thermal property were examined under hydrogen fluoride, hydrogen molecule and carbon (ii) oxide. The study reveals that for a very small value of the modified parameter, the energy eigenvalues of the modified Tietz–Hua potential and that of the actual Tietz–Hua potential are equivalent. Finally, the vibrational energies for Cesium molecule was calculated and compared with the observed value. The calculated results were found to be in good agreement with the observed value.

Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional analysis method

“…The Schrödinger equation (SE) can be studied for different quantum-mechanical processes with the above analytical methods [55][56][57][58]. The analytical solutions to this equation with a physical potential play an important role in our understanding of the foundations of a quantum system.…”

“…The frequently used analytical methods are the Nikiforov-Uvarov method (NU) , Asymptotic iterative method (AIM) [31], Laplace transformation approach [32], ansatz solution method [33], super-symmetric quantum mechanics approach (SUSYQM) [34,35], exact and proper quantization methods [36,37], series expansion method [38][39][40][41][42][43][44][45], the recent study via the Heun function approach has been used widely to study those soluble quantum systems which could not be solved before,e.g. the systems including the Mathieu potential,rigid rotor problem,sextic type problem, Konwent potential and others [46][47][48][49][50][51][52][53][54] The Schrödinger equation (SE) can be studied for different quantum-mechanical processes with the above analytical methods [55][56][57][58]. The analytical solutions to this equation with a physical potential plays an important role in our understanding of the fundamental root of a quantum system.…”

Time correlation function and average energy of molecules in presence of Deng-Fan potential in a moving boundary

“…This has remained an active area of research covering a large span of time, with widespread applications in molecular spectroscopy atom/molecule adsorption on solid surface, deformation of cubic metal, etc. Some important and popular models for vibrational interactions in molecules are as follows: Manning-Rosen [2][3][4][5], Húlthen [6][7][8][9], Woods-Saxon [10,11], Pöschl-Teller [5,12,13], Tietz-Hua [14][15][16], pseudoharmonic [17][18][19], Rosen-Morse [20][21][22], Kratzer [23,24], Eckart [25] and so on.…”

Eigen-solutions and thermal properties of multi-parameter exponential potential

“…Meanwhile, a thorough understanding of molecular structure is dependent on the atom's inter-nuclear interactions and the molecular potential model under consideration [ 1 ]. The Deng-Fan potential [ 2 ], Tietz-Wei potential model [ 3 ], Improved deformed four parameter exponential potential [ 4 ], Tietz-Hua potential [ 5 , 6 , 7 ], Morse and Modified Morse potential [ 8 ], Deng-Fan-Eckart potential [ 9 ], Molecular attractive potential model [ 1 ], Mobius square plus Screened Kratzer potential [ 10 ], Four parameter potential [ 11 ], Varshni potential [ 12 , 13 ], New generalized Morse-like potential exists in various forms in all of these potential models. The various forms of the Morse potential, on the other hand, have been used to investigate the physical behavior of semiconductor surfaces and interfaces [ 14 , 15 , 16 ].…”