We propose a simple analytical model for Harmonic oscillator potential that is associated to the generalized uncertainty principle (GUP) in the presence of energy-dependent mass. A formal condition connected with these systems is based on the mathematical structure of modified quantum mechanics. Consequently, thanks to Feynman’s path integrals formalism, we are able to treat the reorganization of wave functions. Furthermore, in order to convert this path formalism into a local representation, we will use a coordinate transformation method at different usual point interval, which is what these systems assume. In each application, the propagator is calculated, the wave functions and the energy eigenvalues are obtained with the corresponding curves. The special cases are then deduced.

中文翻译：

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具有能量依赖质量的非相对论费曼传播子的 GUP

我们提出了一个简单的谐波振荡器势分析模型，该模型与存在能量依赖质量的广义不确定性原理 (GUP) 相关联。与这些系统相关的形式条件是基于改进的量子力学的数学结构。因此，由于费曼的路径积分形式主义，我们能够处理波函数的重组。此外，为了将这种路径形式转换为局部表示，我们将在不同的常用点间隔处使用坐标变换方法，这就是这些系统所假设的。在每个应用中，传播子都被计算出来，波函数和能量特征值通过相应的曲线得到。然后推导出特殊情况。