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AIP conference proceedings

A Mathematical Method for Exact Analytical Solution of the Schrodinger Equation with Non-central Potential

Mohammad Reza Shojaei, ALI AKBAR RAJABI, Y. Momen, Muhammed Hasan Aslan, Ahmet Yayuz Oral, Mehmet Özer, Süleyman Hikmet Çağlar

Published Jan 1, 2011• 0 citations
Publisher

Abstract

In this paper, we have studied the Schrödinger equation with central and non‐central potential. We have solved the Schrödinger equation in spherical coordinate analytically by using supersymmetric and shape invariance methods. Then we have found the radial and angular parts of wavefunction. Finally the energy eigenvalues of the Schrödinger equation with non‐central potential are obtained.

DOI
10.1063/1.3663100

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In this paper, we have studied the Schrödinger equation with central and non‐central potential. We have solved the Schrödinger equation in spherical coordinate analytically by using supersymmetric and shape invariance methods. Then we have found the radial and angular parts of wavefunction. Finally the energy eigenvalues of the Schrödinger equation with non‐central potential are obtained.
The general solutions of Schrodinger equation for non central potential are obtained by using Nikiforov Uvarov method. The Schrodinger equation with general non central potential is separated into radial and angular parts and energy eigenvalues and eigenfunctions for these potentials are derived analytically. Non central potential is reduced to Coulomb and Hartmann potential by making special selections, and the obtained solutions are compared with the solutions of Coulomb and Hartmann ring shaped potentials given in literature.
The general solutions of the Schrödinger equation for a non-central potential are obtained by using the Nikiforov–Uvarov method. The Schrödinger equation with general non-central potential is separated into radial and angular parts, and energy eigenvalues and eigenfunctions are derived analytically. By making special selections, the non-central potential is reduced to Coulomb and Hartmann ring-shaped potentials, and the obtained results are compared with the solutions of Coulomb and Hartmann potentials given in the literature.
This study presents the solutions of Schrödinger equation for the Non-Central Generalized Inverse Quadratic Yukawa Potential within the framework of Nikiforov-Uvarov. The radial and angular part of the Schrödinger equation are obtained using the method of variable separation. More so, the bound states energy eigenvalues and corresponding eigenfunctions are obtained analytically. Numerical results were obtained for the Generalized Inverse Quadratic Yukawa Potential for comparison sake. It was found out that our results agree with existing literature.
In this paper, we show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in a certain class of noncentral potentials can be easily calculated analytically in a simple and elegant manner by using Supersymmetric method (SUSYQM). We discuss the Poschl-Teller plus Scarf non-central potential systems. Then, by operating the lowering operator we get the ground state wave function, and the excited state wave functions are obtained by operating raising operator repeatedly. The energy eigenvalue is expressed in the closed form obtained using the shape invariant properties. The results are in exact agreement with other methods.Keyword: supersymmetry, non-central potentials, poschl teller plus scarf.
In this paper, we show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in a certain class of noncentral potentials can be easily calculated analytically in a simple and elegant manner by using Supersymmetric method (SUSYQM). We discuss the Poschl-Teller plus Scarf non-central potential systems. Then, by operating the lowering operator we get the ground state wave function, and the excited state wave functions are obtained by operating raising operator repeatedly. The energy eigenvalue is expressed in the closed form obtained using the shape invariant properties. The results are in exact agreement with other methods.Keyword: supersymmetry, non-central potentials, poschl teller plus scarf.