具有狄拉克δ相互作用的等谱势：受约束谱
Isospectral potentials with Dirac delta interaction: Constrained Spectra
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中文总结 AI 辅助
该研究通过不连续超势构造含狄拉克δ函数的等谱量子势，利用边界约束截断能谱，证实局域奇异性可调控量子系统离散能谱，为相关物理系统提供了新途径。
中文摘要 AI 辅助
我们研究包含狄拉克δ函数（DDF）的量子势，该势通过不连续超势在其超对称（等谱）构造中实现，而非简单作为附加部分。该构造包含两个可独立求解的部分，在奇异点处通过对应自伴延拓施加的匹配条件连接。这些边界条件需要仔细正则化，对每个本征态施加独立的代数约束，从而限制并截断能谱。需为偶宇称的存活束缚态数量因此由可用系统参数而非通常的量子化规则确定。将DDF等谱注入简谐振子和Rosen-Morse势的具体案例展示了这种高度受限的能谱，而DDF与Calogero型奇异性的类似组合则因正则化失效而在很大程度上不兼容。因此，局域奇异性能够控制和设计量子系统的离散能谱，可应用于具有极强局域相互作用的众多物理系统。
英文摘要
We study quantum potentials containing Dirac delta function (DDF) within its supersymmetric (isospectral) construction via a discontinuous superpotential, instead of being simply an added part. This construction comprises of two independently solvable sectors joined at the singular point by matching conditions imposed by the corresponding self-adjoint extension. Needing careful regularization, these boundary conditions impose independent algebraic constraints on each of the eigenstates, that restrict and truncate the spectrum. The number of surviving bound states, which are required to be parity-even, is thus fixed by the available system parameters rather than by the usual quantization rule. The specific cases of the Harmonic oscillator and the Rosen-Morse potential isospectrally infused with the DDF demonstrate such highly restrictive spectra, while the similar combination of the DDF with a Calogero-type singularity turns out to be largely incompatible as the regularization breaks down. Therefore, localized singularities are capable of controlling and engineering the discrete spectrum of quantum systems, with possible use in myriads of physical systems with very localized interactions.
发表机构
- Mahidol University（马希托大学）
- Maharaja Sriram Chandra Bhanja Deo University（Maharaja Sriram Chandra Bhanja Deo 大学）
- Indian Institute of Science Education and Research Kolkata（加尔各答印度科学教育与研究学院）
- Siksha O Anusandhan
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