The unified treatment of the non-relativistic bound state solutions, thermodynamic properties, and expectation values of exponential-type potentials

Abstract

In this paper, we obtained the analytical N-dimensional bound state solutions of exponential-type potential functions using the semi-classical WKB approximation method with an improved approximation to the orbital centrifugal barrier. Furthermore, we derived the partition function with the associated thermodynamic properties. We calculated the expectation values (⟨1/r^2 ⟩ ) via the Hellmann-Feynman theorem. Our results for the energy levels are in excellent agreement compared to the best available results obtained by other methods in the existing literature. The variations of the thermodynamic functions with the temperature parameter (β) agree very well with the other results obtained under different potential energy functions. The expectation values conformed to the ones obtained by another approach in previous work. This work demonstrates the exactness of the leading order WKB approximation.

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

“…( 14) in conjunction with Eqs. ( 9), ( 10), (11), and ( 12), the two partner potentials of the supersymmetry quantum mechanics can fully be written in the form…”

“…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 ].…”

“…Omugbe et al. [ 11 ] investigated the unified treatment of non-relativistic bound state solutions, thermodynamic properties, and expectation values of exponential type potentials within the framework of the semi-classical WKB approach. On a general ground several studies have been reported on the Schrödinger equation for some potentials [ 25 , 26 , 27 , 28 ].…”

“…Okorie et al [24] investigated the thermodynamic properties of the improved deformed exponential-type potential (IDEP) for some diatomic systems, they obtained the ro-vibrational energy spectra of the potential model using coordinate transformation and the Greene-Aldrich approximation to centrifugal term. Omugbe et al [11] investigated the unified treatment of non-relativistic bound state solutions, thermodynamic properties, and expectation values of exponential type potentials within the framework of the semi-classical WKB approach. On a general ground several studies have been reported on the Schr€ odinger equation for some potentials [25,26,27,28].…”

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

“…They presented energy eigenvalue in a close form in order to obtain partition function and other thermodynamic properties. Omugbe et al [55] recently studied the unified treatment of the nonrela-tivistic bound state solutions, thermodynamic properties, and expectation values of exponential-type potentials where they obtained the thermodynamic properties within the framework of semiclassical WKB approach. The authors studied the special cases of the potential as Eckart, Manning-Rosen, and Hulthen potentials.…”