Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential

doi:10.1088/1674-1056/abe371

中国物理B ›› 2021, Vol. 30 ›› Issue (7): 70301-070301.doi: 10.1088/1674-1056/abe371

Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential

Eyube E S^1,†, Rawen B O², and Ibrahim N³

1 Department of Physics, School of Physical Sciences, Modibbo Adama University of Technology, P M B 2076 Yola, Adamawa State, Nigeria;
2 Directorate of Basic and Remedial Studies, Abubakar Tafawa Balewa University(ATBU), P M B 750001, Bauchi, Bauchi State, Nigeria;
3 Department of Physics, Faculty of Science, P M B 1069, Maiduguri, Borno State, Nigeria

收稿日期:2020-11-22 修回日期:2021-01-11 接受日期:2021-02-08 出版日期:2021-06-22 发布日期:2021-06-26
通讯作者: Eyube E S E-mail:edwineyubes@mautech.edu.ng

Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential

Eyube E S^1,†, Rawen B O², and Ibrahim N³

1 Department of Physics, School of Physical Sciences, Modibbo Adama University of Technology, P M B 2076 Yola, Adamawa State, Nigeria;
2 Directorate of Basic and Remedial Studies, Abubakar Tafawa Balewa University(ATBU), P M B 750001, Bauchi, Bauchi State, Nigeria;
3 Department of Physics, Faculty of Science, P M B 1069, Maiduguri, Borno State, Nigeria

Received:2020-11-22 Revised:2021-01-11 Accepted:2021-02-08 Online:2021-06-22 Published:2021-06-26
Contact: Eyube E S E-mail:edwineyubes@mautech.edu.ng

摘要/Abstract

摘要： The Schrödinger equation is solved with general molecular potential via the improved quantization rule. Expression for bound state energy eigenvalues, radial eigenfunctions, mean kinetic energy, and potential energy are obtained in compact form. In modeling the centrifugal term of the effective potential, a Pekeris-like approximation scheme is applied. Also, we use the Hellmann-Feynman theorem to derive the relation for expectation values. Bound state energy eigenvalues, wave functions and meanenergies of Woods-Saxon potential, Morse potential, Möbius squared and Tietz-Hua oscillators are deduced from the general molecular potential. In addition, we use our equations to compute the bound state energy eigenvalues and expectation values for four diatomic molecules viz. H₂, CO, HF, and O₂. Results obtained are in perfect agreement with the data available from the literature for the potentials and molecules. Studies also show that as the vibrational quantum number increases, the mean kinetic energy for the system in a Tietz-Hua potential increases slowly to a threshold value and then decreases. But in a Morse potential, the mean kinetic energy increases linearly with vibrational quantum number increasing.

关键词: general molecular potential, Schr?dinger equation, improved quantization rule

Abstract: The Schrödinger equation is solved with general molecular potential via the improved quantization rule. Expression for bound state energy eigenvalues, radial eigenfunctions, mean kinetic energy, and potential energy are obtained in compact form. In modeling the centrifugal term of the effective potential, a Pekeris-like approximation scheme is applied. Also, we use the Hellmann-Feynman theorem to derive the relation for expectation values. Bound state energy eigenvalues, wave functions and meanenergies of Woods-Saxon potential, Morse potential, Möbius squared and Tietz-Hua oscillators are deduced from the general molecular potential. In addition, we use our equations to compute the bound state energy eigenvalues and expectation values for four diatomic molecules viz. H₂, CO, HF, and O₂. Results obtained are in perfect agreement with the data available from the literature for the potentials and molecules. Studies also show that as the vibrational quantum number increases, the mean kinetic energy for the system in a Tietz-Hua potential increases slowly to a threshold value and then decreases. But in a Morse potential, the mean kinetic energy increases linearly with vibrational quantum number increasing.

Key words: general molecular potential, Schr?dinger equation, improved quantization rule

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

03.65.Ta (Foundations of quantum mechanics; measurement theory) 03.65.-w (Quantum mechanics) 34.20.Cf (Interatomic potentials and forces)

Eyube E S, Rawen B O, and Ibrahim N. Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential[J]. 中国物理B, 2021, 30(7): 70301-070301.

Eyube E S, Rawen B O, and Ibrahim N. Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential[J]. Chin. Phys. B, 2021, 30(7): 70301-070301.

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Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential

Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential

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