Noncommutativity of position and momentum makes it difficult to formulate the unambiguous structure of the kinetic part of Hamiltonian for the position-dependent effective mass (PDEM). Various existing proposals of writing the viable kinetic part of the Hamiltonian for PDEM conceptually lack from first principle calculation. Starting from the first principle calculation, in this article, we have advocated the proper self-adjoint form of the kinetic part of Hamiltonian for PDEM. We have proposed that ambiguity of construction of viable kinetic part for PDEM can be avoided if one takes the care from the classical-level combination of position and momentum. In the quantum level, the spatial points do not appear in equivalent footing for the measure of inertia (mass). This exhibits the existence of an inertia potential. Thus, the new structure of the kinetic part differs from the existing structure of the kinetic part of Hamiltonian by providing an extra potential like contribution. This inertia potential can be absorbed with the external potential, and the known structure of PDEM can be redefined under this effective potential. This enables us to apply the existing formalism of quantum mechanics. The coherent state structures for the newly proposed form of Hamiltonian are provided for a few simple experimentally important models.

位置和动量的不可交换性使得很难为位置相关有效质量（PDEM）公式化汉密尔顿动力学部分的明确结构。从第一原理计算上，在概念上缺乏为PDEM编写汉密尔顿方程的可行动力学部分的各种现有建议。从第一个原理计算开始，在本文中，我们提倡PDEM的哈密顿动力学部分的适当自伴随形式。我们已经提出，如果人们将位置和动量的经典层次结合起来，就可以避免为PDEM构造动力学部分的模棱两可。在量子水平上，对于惯性（质量）的度量，空间点不会以等效的立足点出现。这表明存在惯性势。从而，动力学部分的新结构与哈密顿量动力学部分的现有结构有所不同，因为它提供了额外的潜在贡献。该惯性电势可以被外部电势吸收，并且PDEM的已知结构可以在此有效电势下重新定义。这使我们能够应用现有的量子力学形式主义。新提出的哈密顿量形式的相干态结构提供了一些简单的实验重要模型。这使我们能够应用现有的量子力学形式主义。新提出的哈密顿量形式的相干态结构提供了一些简单的实验重要模型。这使我们能够应用现有的量子力学形式主义。新提出的哈密顿量形式的相干态结构提供了一些简单的实验重要模型。