Schrödinger equation with position-dependent mass (PDM) allows the identification of quantum wave functions in a complex environment. Following the progress of this investigation field, in this work, we consider the non-Hermitian kinetic operators associated with the PDM Schrödinger equation. We provide a simplified picture for PDM quantum systems that admit exact solutions in confining potentials. First, we investigate the solutions for a sinusoidal and an exponential PDM distributions in an infinite potential well. Next, we consider the solutions for a PDM harmonic oscillator potential associated with a power-law PDM distribution. The results presented in this work offer a way to approach new classes of solutions for PDM quantum systems in confining potential (bound states). Complementarily, we interpret the quantum partition function of the canonical ensemble of a PDM system in the context of the superstatistics, which, in turn, allows us to express the inhomogeneity of the PDM in terms of beta distribution \(f(\beta )\), Dirac delta distributions for \(f(\beta )\), and effective temperatures. Our results are, hereby, reported for the sinusoidal and the exponential PDM distributions.

具有位置相关质量（PDM）的Schrödinger方程可识别复杂环境中的量子波函数。随着研究领域的发展，在这项工作中，我们考虑了与PDMSchrödinger方程相关的非Hermitian动力学算子。我们为PDM量子系统提供了一张简化的图，该图接受了限制电位的精确解决方案。首先，我们研究无限势阱中正弦和指数PDM分布的解。接下来，我们考虑与功率定律PDM分布相关的PDM谐波振荡器电位的解决方案。这项工作中提出的结果提供了一种在势能（束缚态）中接近PDM量子系统的新型解决方案的方法。相辅相成\（F（\测试版）\） ，为狄拉克δ分布\（F（\测试版）\） ，和有效的温度。因此，我们的结果报告为正弦曲线和指数PDM分布。