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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.05899 |
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| _version_ | 1866912179468369920 |
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| author | Lima, F. C. E. Belchior, F. M. Almeida, C. A. S. |
| author_facet | Lima, F. C. E. Belchior, F. M. Almeida, C. A. S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05899 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the singular position-dependent mass Lima, F. C. E. Belchior, F. M. Almeida, C. A. S. Quantum Physics High Energy Physics - Theory 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. |
| title | On the singular position-dependent mass |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.05899 |