Ro‐vibrational energy and thermodynamic properties of molecules subjected to Deng–Fan potential through an improved approximation

Abstract

Accurate solution of the Schrödinger equation with Deng-Fan potential is presented by means of Nikiforov-Uvarov method. A modified Pekeris-type approximation is proposed for the centrifugal term, from a linear combination of the r ! 0 and r ! r e limits. It can potentially offer a series of approximations (depending on an adjustable parameter λ). The existing approximations in the literature can then be recovered in certain special cases. Its efficiency and feasibility is demonstrated by a critical comparison of eigenvalues produced at various λ's for four molecules, namely, H 2 , LiH, HCl and CO. Analytical expressions are derived for energies, eigenfunctions and the thermodynamic properties such as vibrational mean free energy, vibrational free energy, vibrational entropy and vibrational specific heat. The effect of quantum correction on partition function and thermodynamic properties is discussed by including the correction up to 10th-order, for H 2 and LiH. The effect of λ parameter on these properties is also studied.

Comparison between time-independent and time-dependent quantum systems in the context of energy, Heisenberg uncertainty, average energy, force, average force and thermodynamic quantities

“…The comparisons of thermodynamic quantities at high-temperature among four quantum systems are shown in Eq. (53). As an extension of this work, one can be studied to construct higher-dimensional time-dependent quantum systems at high as well as low temperature, if the scale factor L is twice continuously differentiable.…”

“…[51]. Also, partition function can be expresses as a series which is calculated by Poisson summation formula [52,53]. In this paper, we will use the Euler-Maclaurin summation formula over a finite as well as an infinite domain.…”

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

“…( 10) are obtained within a recently proposed scheme combining both Pekeris [70] and Greene-Aldrich [71] approximations. This has lead to a very satisfactory treatment of potential throughout the whole domain of consideration [5,25,42,72,73]. Therefore, solution of Eq.…”

Nonrelativistic solutions of Schrödinger equation and thermodynamic properties with the proposed modified Mobius square plus Eckart potential

“…Similarly, the energy spectra and thermodynamic properties of the HCl, H 2 , CO and LiH molecules with the hyperbolic Poschl-Teller potential have been studied [34] . On a similar note, Nath and Roy [35] studied the thermodynamic properties of the same set of molecules under the Deng-Fan potential. Also, Bakhati and co-workers [36] , computed the thermodynamic properties of the light gases, O 2 and H 2 .…”