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Journal of Physics Conference Series

The solution of 4-dimensional Schrodinger equation for polynomial inverse potential and its partner potential by using ansatz wavefunction method

Suparmi Suparmi, C. Cari, Wahyulianti, Kristiana Nathalia Wea

Published Mar 1, 2018• 0 citations
Publisher

Abstract

The radial part of 4-dimensional Schrodinger equation for Polynomial Inverse potential and its partner potential was solved by using the Ansatz Wavefunction method. By applying of the properties and operators of the Supersymmetric Quantum Mechanic method the partner potential was constructed. The eigenvalues and eigenfunctions of the Polynomial Inverse potential and the eigenvalues and eigenfunctions of its partner potential were different. The partner potential of Polynomial Inverse potential for n > 1 has eigenvalue greater than Polynomial Inverse potential as its original potential.

DOI
10.1088/1742-6596/997/1/012051

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The radial part of 4-dimensional Schrodinger equation for Polynomial Inverse potential and its partner potential was solved by using the Ansatz Wavefunction method. By applying of the properties and operators of the Supersymmetric Quantum Mechanic method the partner potential was constructed. The eigenvalues and eigenfunctions of the Polynomial Inverse potential and the eigenvalues and eigenfunctions of its partner potential were different. The partner potential of Polynomial Inverse potential for n > 1 has eigenvalue greater than Polynomial Inverse potential as its original potential.
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The angular part of 4-dimensional Schrodinger equation for Scarf potential was solved by using the Nikiforov-Uvarov method and Supersymmetric Quantum Mechanic method. The determination of the ground state wave function has been used Nikiforov-Uvarov method and by applying the parametric generalization of the hypergeometric type equation. By using manipulation of the properties and operators of the Supersymmetric Quantum Mechanic method the partner potential was constructed. The ground state wave functions of original Scarf potential is different than the ground state wave functions of the construction result potential.
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Bound state solutions of square root power law potential--Wavefunction ansatz method on DDD-dimensional Schrödinger equation
DDD-dimensional Schrödinger equation is addressed for square root power law potential. Bound state unnormalized eigenfunctions and the energy eigenvalues are obtained using wave function ansatz method. Some special cases are studied at the end to ensure the correctness of present work.