几种模型哈密顿量的离散谱的计数算符分析
Counting operator analysis of the discrete spectrum of some model Hamiltonians
摘要：
在任何模型哈密尔顿算子H的谱的计数算子分析中，第一步是选择厄米算子M，使得与H的第三个交换子与第一个交换子成比例。接下来计算算子R和R^ \dagger，它们共享创建算子和湮灭算子的一些性质，并且使得$M$成为计数算子。然后，H的谱被分解成多重态，多重态不是由H的对称性决定的，而是由参考哈密顿量H_ref的对称性决定的，参考哈密顿量H_ref由H_ref=H-R-R^ \dagger定义，并且与M交换。最后，我们介绍了稳定本征态的概念。结果表明，在较弱的条件下，一个稳定的本征态可以用来构造另一个本征态。
英文摘要：
The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates operators R and R^\dagger which share some of the properties of creation and annihilation operators, and such that $M$ becomes a counting operator. The spectrum of H is then decomposed into multiplets, not determined by the symmetries of H, but by those of a reference Hamiltonian H_ref, which is defined by H_ref=H-R-R^\dagger, and which commutes with M. Finally, we introduce the notion of stable eigenstates. It is shown that under rather weak conditions one stable eigenstate can be used to construct another one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
