J—state solutions and thermodynamic properties of the Tietz oscillator

Abstract

In this work, we have solved the radial part of the Schrödinger equation with Tietz potential to obtain explicit expressions for bound state ro-vibrational energies and radial eigenfunctions. The proper quantization rule and ansatz solution technique were used to arrive at the solutions. In modeling the pseudo-spin–orbit term of the effective potential, the Pekeris-like and the Greene-Aldrich approximation recipes were applied. Using our equation for eigen energies, we have deduced expression for bound state energy eigenvalues of Deng-Fan oscillator. The result obtained agrees with available literature data for this potential. Also, for arbitrary values of rotational and vibrational quantum numbers, we have calculated bound state energies for the Tietz oscillator. Our computed results are in excellent agreement with those in the literature. Furthermore, the result showed that unlike Greene-Aldrich approximation, energies computed based on Pekeris-like approximation are better and almost indistinguishable from numerically obtained energies of the Tietz oscillator in the literature. With the help of our formula for ro-vibrational energy, analytical expressions for some important thermodynamic relations were also derived for the Tietz oscillator. The derived thermal functions which include ro-vibrational: partition function, free energy, mean energy, entropy and specific heat capacity were subsequently applied to the spectroscopic data of KI diatomic molecule. Studies of the thermal functions indicated that the partition function decreases monotonically as the temperature is raised and increases linearly for increase in the upper bound vibrational quantum number. On the other hand, increase in either temperature or upper bound vibrational quantum number amounts to monotonic rise in the entropy of the KI molecules

Thermodynamic relations and ro-vibrational energy levels of the improved Pöschl–Teller oscillator for diatomic molecules

“…Several solution methods have been proposed and used to solve the Schrödinger equation, some of the solution techniques include: ansatz technique [8], 1/N expansion method [9], asymptotic iteration method [10,11], Nikiforov-Uvarov method [12], exact quantization rule [13][14][15], proper (or improved) quantization rule [16,17] and supersymmetric quantum approach [18] among others.…”

Thermodynamic functions of the improved Scarf II oscillator

“…Quite a number of diatomic molecule oscillators have been used to describe the internal vibration of diatomic and triatomic molecules. With the help of this representation, various analytical equations have been derived and used to predict the thermal properties of a substance [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

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

“…Furthermore, thermodynamic properties of screened Kratzer potential in the presence of magnetic and Aharanov-Bohm fields have been reported [37] . Recent works on thermodynamic properties of various systems have been reported [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] .…”