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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >On the exact solutions of the Dirac equation with a novel angle-dependent potential
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On the exact solutions of the Dirac equation with a novel angle-dependent potential

机译：关于具有新型角度相关势的Dirac方程的精确解

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摘要

We study the problem of the relativistic motion of a 1/2-spin particle in an exactly solvable potential, which consists of the harmonic oscillator potential plus a novel angle-dependent potential, V(r,theta) = 1/2M omega(2)r(2) + h(2)c(2)/r(2) (gamma + beta sin(2)theta + alpha sin(4)theta/sin(2)theta cos(2)theta). The analytic bound state solutions of the Dirac equation for this potential are obtained by using the Nikiforov-Uvarov method. The wave functions of the radial and angle-dependent parts of the Dirac equation are derived in the form of the Laguerre and Jacobi polynomials. The contribution of the angle-dependent potential to the relativistic energy spectra is discussed under the condition that the scalar potential is equal to or minus the vector potential.
机译：我们研究了在精确可解电势中1/2自旋粒子的相对论运动问题，该问题包括谐波振荡器电势以及新的与角度相关的电势，V（r，theta）= 1 / 2M omega（2 ）r（2）+ h（2）c（2）/ r（2）（γ+ beta sin（2）theta + alpha sin（4）theta / sin（2）theta cos（2）theta）。通过使用Nikiforov-Uvarov方法获得了Dirac方程对此势的解析束缚态解。 Dirac方程的径向和角度相关部分的波函数以Laguerre和Jacobi多项式的形式导出。在标量电势等于或减去矢量电势的条件下，讨论了角度相关电势对相对论能谱的贡献。

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