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Isospectral mapping for quantum systems with energy point spectra to polynomial quantum harmonic oscillators
Physics Letters A ( IF 2.3 ) Pub Date : 2021-01-09 , DOI: 10.1016/j.physleta.2021.127144
Ole Steuernagel , Andrei B. Klimov

We show that a polynomial Hˆ(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice leads to a re-ordering of the associated energy eigenfunctions of Hˆ such that the number of their nodes does not increase monotonically with increasing level number. Systems Hˆ have certain ‘universal’ features, we study their basic behaviours.



中文翻译:

具有能量点谱的量子系统的等谱映射到多项式量子谐波振荡器

我们证明了一个多项式 HˆñÑ谐波振荡器哈密顿的允许我们设计的量,第一完全解连续量子系统Ñ离散能量本征值可以随意选择。通常,这种选择导致对相关的能量本征函数的重新排序。Hˆ这样,其节点数不会随级别数的增加而单调增加。系统篇Hˆ 具有某些“通用”特征,我们研究它们的基本行为。

更新日期:2021-01-14
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