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Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics
Advances in High Energy Physics ( IF 1.7 ) Pub Date : 2021-02-16 , DOI: 10.1155/2021/8830063
A. I. Ahmadov 1, 2 , S. M. Aslanova 1 , M. Sh. Orujova 3 , S. V. Badalov 4
Affiliation  

The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound state problem is the Klein-Fock-Gordon equation. In this work, using a developed scheme, we present how to surmount the centrifugal part and solve the modified Klein-Fock-Gordon equation for the linear combination of Hulthén and Yukawa potentials. In particular, we show that the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept. Here, both scalar potential conditions, which are whether equal and nonequal to vector potential, are considered in the calculation. The energy levels and corresponding normalized eigenfunctions are represented as a recursion relation regarding the Jacobi polynomials for arbitrary states. Beyond that, a closed form of the normalization constant of the wave functions is found. Furthermore, we state that the energy eigenvalues are quite sensitive with potential parameters for the quantum states. The nonrelativistic and relativistic results obtained within SUSY QM overlap entirely with the results obtained by ordinary quantum mechanics, and it displays that the mathematical implementation of SUSY quantum mechanics is quite perfect.

中文翻译:

SUSY量子力学中Hulthén和Yukawa势之和的Klein-Fock-Gordon方程的解析束缚态解

相对论波动方程在量子场论的背景下确定了量子场的动力学。Klein-Fock-Gordon方程是处理相对论束缚态问题的常规工具之一。在这项工作中,我们使用一种已开发的方案,介绍了如何克服离心部分并求解修正的Klein-Fock-Gordon方程,以实现Hulthén和Yukawa势的线性组合。特别地,我们表明,相对论能量本征值和相应的径向波函数是通过应用形状不变性概念从超对称量子力学获得的。在此,在计算中考虑两个标量势条件,即是否等于和不等于矢量势。状态。除此之外,找到了波动函数归一化常数的封闭形式。此外,我们指出,能量特征值对于量子态的潜在参数非常敏感。SUSY QM中获得的非相对论和相对论结果与普通量子力学获得的结果完全重叠,这表明SUSY量子力学的数学实现是相当完善的。
更新日期:2021-02-16
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