In the context of quantum mechanics reformulated in a modified Hilbert space, we can formulate the Feynman’s path integral approach for the quantum systems with position-dependent mass particle using the formulation of position-dependent infinitesimal translation operator. Which is similar a deformed quantum mechanics based on modified commutation relations. An illustration of calculation is given in the case of the harmonic oscillator, the infinite square well and the inverse square plus Coulomb potentials.

中文翻译：

---

位移算子方法中具有位置依赖质量的量子动力学的路径积分

在改进的希尔伯特空间中重新表述的量子力学的背景下，我们可以使用位置相关的无穷小平移算子的公式来制定具有位置相关质量粒子的量子系统的费曼路径积分方法。这类似于基于修正对向关系的变形量子力学。在谐振子、无限平方阱和平方反比加库仑势的情况下给出了计算说明。