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arXiv · 2406.05899

On the singular position-dependent mass

F. C. E. Lima·F. M. Belchior·C. A. S. Almeida
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Abstract

Revisiting the issue associated with Position-Dependent Mass (PDM), we reaffirm that the appropriate framework for addressing a generic PDM is the symmetrization proposed by BenDaniel and Duke. To accomplish this result adopts the effective mass Hamiltonian proposed by von Roos, corrected by a symmetrized kinematic term. After verifying the appropriate ordering to approach the PDM issue, one investigates a crystalline lattice with a defect described by a singular PDM. The singular mass profile proves intriguing as it yields an atom's cluster in the neighborhood of the singularity. Considering that a restoring force acts on the atoms, one notes that the confluent Heun function describes the quantum states. Furthermore, one highlights that when the effective mass distribution tends to a constant profile, we recover a system similar to the harmonic oscillator.

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F. C. E. Lima, F. M. Belchior, C. A. S. Almeida. 2024-06-09. On the singular position-dependent mass. https://doi.org/10.1088/1402-4896%2Fad9c2d

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