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AIP conference proceedings

Study of the Dirac equation with the position-dependent mass for modified manning Rosen potential using Laplace method

Suparmi Suparmi, L. K. Permatahati, C. Cari

Published Jan 1, 2023• 1 citation
Publisher

Abstract

We study the Dirac equation with position dependent mass (PDM) for Modified Manning Rosen potential. The Dirac equation with PDM is solved using Laplace method to obtain the energy equation and the wave function. We calculate the energy eigenvalues and the wave function numerically for several quantum numbers and parameters potential. The results showed that the energy eigenvalue increases as the quantum number and the parameters potential increase. The variation of the parameter potential gives the different of waveforms in each state.

DOI
10.1063/5.0178343

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In this paper, Schrodinger equation has been solved analytically with position dependent mass by the Rosen-Morse potential. The position dependent mass defined as the function 1/(1 — tanh(η x )). Then corresponding position dependent mass substituted into Schrodinger equation. After that the obtained equation compared with associated Jacobi differential equation. Therefore, the eigenvalue and eigenfunctionhave been calculated, and from there the bound state has been found in terms of quantum numbers and the coefficients of potential. Also, the wave function has been obtained in terms of the associated Jacobi equation by μ = —3 and v = 2.
An approximate method is proposed to solve the position-dependent mass (PDM) Schrödinger equation. The procedure suggested here leads to the solution of the PDM Schrödinger equation without transforming the potential function to the mass space or vice versa. The method based on the asymptotic Taylor expansion of the function produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the PDM Schrödinger equation. The results show that the PDM and constant mass Schrödinger equations are not isospectral. The calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm.
An approximate method is proposed to solve position dependent mass Schrodinger equation. The procedure suggested here leads to the solution of the PDM Schrodinger equation without trans- forming the potential function to the mass space or vice verse. The method based on asymptotic Taylor expansion of the function, produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the PDM Schrodinger equation. The results show that PDM and constant mass Schrodinger equations are not isospectral. The calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm.
In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.