One-dimensional quantum well with charges on the walls

IF 2.9 3区物理与天体物理 Q3 NANOSCIENCE & NANOTECHNOLOGY

Physica E-low-dimensional Systems & Nanostructures Pub Date : 2025-08-05 DOI:10.1016/j.physe.2025.116348

Sergo Rekhviashvili, Arsen Pskhu

引用次数: 0

Abstract

We present an analytical investigation of an electron confined in a one-dimensional quantum well with a potential generated by two fixed positive charges at the boundaries. This system combines hard-wall confinement with long-range Coulomb interaction. By solving the stationary Schrödinger equation using convergent power series, we derive exact wavefunctions and energy levels. The energy spectrum contains both positive and negative values, depending on the well width. Notably, for a discrete set of well widths corresponding to triangular-number multiples of the Bohr radius, the ground state energy becomes exactly zero. These results provide a solvable model for confined Coulomb systems and offer insight into size quantization effects relevant to low-dimensional semiconductor structures, quantum dots, and high-pressure hydrides.

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带电荷的一维量子阱

我们提出了一维量子阱中由边界处两个固定正电荷产生电位的电子的分析研究。该系统结合了硬壁约束和远距离库仑相互作用。通过收敛幂级数求解平稳Schrödinger方程，我们得到了精确的波函数和能级。能谱包含正值和负值，这取决于井的宽度。值得注意的是，对于与玻尔半径的三角数倍相对应的离散井宽集，基态能量正好变为零。这些结果为受限库仑系统提供了一个可求解的模型，并为与低维半导体结构、量子点和高压氢化物相关的尺寸量子化效应提供了见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica E-low-dimensional Systems & Nanostructures 物理-纳米科技

CiteScore

7.30

自引率

6.10%

发文量

356

审稿时长

65 days

期刊介绍： Physica E: Low-dimensional systems and nanostructures contains papers and invited review articles on the fundamental and applied aspects of physics in low-dimensional electron systems, in semiconductor heterostructures, oxide interfaces, quantum wells and superlattices, quantum wires and dots, novel quantum states of matter such as topological insulators, and Weyl semimetals. Both theoretical and experimental contributions are invited. Topics suitable for publication in this journal include spin related phenomena, optical and transport properties, many-body effects, integer and fractional quantum Hall effects, quantum spin Hall effect, single electron effects and devices, Majorana fermions, and other novel phenomena. Keywords: • topological insulators/superconductors, majorana fermions, Wyel semimetals; • quantum and neuromorphic computing/quantum information physics and devices based on low dimensional systems; • layered superconductivity, low dimensional systems with superconducting proximity effect; • 2D materials such as transition metal dichalcogenides; • oxide heterostructures including ZnO, SrTiO3 etc; • carbon nanostructures (graphene, carbon nanotubes, diamond NV center, etc.) • quantum wells and superlattices; • quantum Hall effect, quantum spin Hall effect, quantum anomalous Hall effect; • optical- and phonons-related phenomena; • magnetic-semiconductor structures; • charge/spin-, magnon-, skyrmion-, Cooper pair- and majorana fermion- transport and tunneling; • ultra-fast nonlinear optical phenomena; • novel devices and applications (such as high performance sensor, solar cell, etc); • novel growth and fabrication techniques for nanostructures