The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

Pramana

Amlan K Roy1 2¹ 

[1] Department of Chemistry, University of New Brunswick, Fredericton, NB, E3B 6E2, Canada$$

关键词: Generalized pseudospectral method;    Hulthén potential;    Yukawa potential.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The generalized pseudospectral (GPS) method is employed to calculate the bound states of the Hulthén and the Yukawa potentials in quantum mechanics, with special emphasis on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a non-uniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials with 𝑛 ≤ 10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high as 𝑛 = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. The 𝑛 > 6 states of the Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1𝑠 and 2𝑠 states of the Yukawa potential, the present method surpasses the accuracy of all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials.

【 授权许可】

Unknown