In this study, nonlocal phenomena in quantum mechanics are investigated by making use of fractional calculus. in this context, fractional creation and annihilation operators are introduced and quantum mechanical harmonic oscillator has been generalized as an important tool in quantum field theory. Therefore wave functions and energy eigenvalues of harmonic oscillator are obtained with respect to the order of fractional derivative which corresponds to influence of nonlocal effects. In order to investigate nonlocality in quantum field theory, Einstein's coefficients are taken into consideration in the framework of fractional calculus. For this purpose, all energy modes of photons are considered as fractional quantized harmonic oscillators and thus Einstein's coefficients are obtained. In the case α = 1, where space becomes continuous, results of conventional physical models are recovered.

中文翻译：

---

带有分数阶微积分的量子力学中的非局域现象

本研究利用分数阶微积分研究量子力学中的非局域现象。在此背景下，分数创建和湮灭算符被引入，量子力学谐振子已被推广为量子场论中的重要工具。因此，谐振子的波函数和能量特征值是相对于对应于非局域效应影响的分数阶导数获得的。为了研究量子场论中的非定域性，在分数阶微积分的框架内考虑了爱因斯坦系数。为此，光子的所有能量模式都被视为分数量子化的谐振子，从而获得爱因斯坦系数。在 α = 1 的情况下，空间变得连续，