In this study, we have extended the idea of fractional spin introduced recently in literature based on two orders fractional derivative operator. Generalizations of the fractional spin, the fractional angular momentum and the fractional momentum operators were obtained. The theory is characterized by a noncommutativity between the generalized fractional angular momentum and the fractional Hamiltonian. We have derived the corresponding fractional Schrodinger equation and we have discussed its implications on the problems of a free particle and a particle moving in an infinite well potential. Enhancements of their corresponding energies levels and ground energies were observed which are in agreement with phenomenological theories such as noncommutative quantum mechanics.

中文翻译：

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量子力学中广义分数自旋、分数角动量、分数动量算子

在这项研究中，我们扩展了最近在基于二阶分数阶导数算子的文献中引入的分数自旋的思想。得到了分数自旋、分数角动量和分数动量算子的推广。该理论的特点是广义分数角动量和分数哈密顿量之间的非对易性。我们已经推导出相应的分数薛定谔方程，并讨论了它对自由粒子和在无限势阱中运动的粒子问题的影响。观察到它们相应的能级和基能的增强，这与非对易量子力学等现象学理论一致。