相对论性夸克模型的分数阶Nikiforov-Uvarov方法描述
On a Relativistic Quark Model Description via the Fractional Nikiforov-Uvarov Method
摘要：
Dirac方程在相对论量子系统中起着至关重要的作用，当选择某一势的类型作为Cornell势时，Dirac方程可化为类似于Schrodinger方程的形式。通过选择广义分数阶导数，分数阶Nikiforov-Uvarov方法作为一个很好的有效工具。通过解析求解Dirac方程，得到了分数阶形式下的能量本征值和相应的波函数。得到了与经典模型相容的特殊情形。分数阶Dirac方程的求解将为经典相对论量子系统的求解和结果的改进开辟一条新的途径。
英文摘要：
The Dirac equation plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrodinger equation when a certain potential's type is selected as the Cornell potential. By choosing the generalized fractional derivative, the fractional Nikiforov-Uvarov method is applied as a good efficient tool. The energy eigenvalues and corresponding wave functions are obtained in the sense of fractional forms by solving Dirac equation analytically. The special case is obtained, which is compatible with the classical model. Solving the fractional Dirac equation will open a new path to solve and improve results in the classical relativistic quantum systems.
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