Approximate analytical solution of the Dirac equation for pseudospin symmetry with modified Po schl-Teller potential and trigonometric Scarf II non-central potential using asymptotic iteration method

6th Asian Physics Symposium

Pratiwi, B.N.^1 ; Suparmi, A.^1,2 ; Cari, C.^1,2 ; Husein, A.S.^2 ; Yunianto, M.^1

Physics Department, Faculty of Mathematics and Science, Sebelas Maret University, Jl.Ir. Sutami 36A, Kentingan Surakarta

57126, Indonesia^1

Physics Department, Graduate Program, Sebelas Maret University, Indonesia^2

关键词: Approximate analytical solutions;    Asymptotic iteration method;    Central potentials;    Hypergeometric functions;    Matlab- software;    Quantum numbers;    Relativistic energy;    Variable substitution;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/739/1/012020/pdf
DOI  :  10.1088/1742-6596/739/1/012020

来源: IOP

【 摘 要 】

We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number nrcauses decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions.