Abstract
The approximate solutions of Schrodinger equation for the Hua plus modified Eckart (HPME) potential is obtained via the Formula method. The vibrational partition function and other thermodynamic properties were investigated. Using the Hellmann-Feynman theorem, the expectation values of r -2, T and p2 and their numerical values are also presented. Some cases of this potential are also studied. The results of our study are consistent with those in literature.
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.
The focus of discussion in Working Group 3 was on the Thermodynamic Properties as determined spectroscopically, including the observational techniques and the theoretical modeling of physical processes responsible for the emission spectrum. Recent advances in observational techniques and theoretical concepts make this discussion particularly timely. It is wise to remember that the determination of thermodynamic parameters is not an end in itself and that these are interesting chiefly for what they can tell us about the energetics and mass transport in prominences.
Approximate Solutions, Thermodynamic Properties and Expectation Values With the Hua Plus Modified Eckart (HPME) Potential
