arXiv 0907.17362009-07-10quant-phhep-th

自伴Calogero Hamilton算子的大振子表示

Large Oscillator representations for self-adjoint Calogero Hamiltonians

D. M. Gitman, I. V. Tyutin, B. L. Voronov

摘要：

在文章arXiv：0903.5277 [quant-ph]中，我们对粒子在Calogero势$V(x)=αx^{-2}$中的一维运动进行了数学上严格的量子力学处理。这样，我们已经描述了所有可能的s.a.运营商（s.a. Hamilton算子）与Calogero Hamilton算子的形式微分表达式$\check{H}=-d_{x}^{2}+αx^{-2}$相关联。在这里，我们讨论一个新的方面的问题，所谓的振荡器表示的Calogero哈密顿。众所周知，形式为$\hat{N}=\hat{a}^{+}\hat{a}$和$\hat{A}=\hat{a}\hat{a}^{+}$的算子称为振荡器型算子。如果初等算子$\hat{a}$和$\hat{a}^{+}$是稠密定义的，则振子型算子服从几个有用的性质。结果是一些s.a. Calogero Hamilton算子是振子型算子。我们描述这样的哈密顿算子，并找到相应的相互伴随的基本运营商。

英文摘要：

In the article arXiv:0903.5277 [quant-ph], we have presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential $V(x)=αx^{-2}$. In such a way, we have described all possible s.a. operators (s.a. Hamiltonians) associated with the formal differential expression $\check{H}=-d_{x}^{2}+αx^{-2}$ for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representation for the Calogero Hamiltonians. As it is know, operators of the form $\hat{N}=\hat{a}^{+}\hat{a}$ and $\hat{A}=\hat{a}\hat{a}^{+}$ are called operators of oscillator type. Oscillator type operators obey several useful properties in case if the elementary operator $\hat{a}$ and $\hat{a}^{+}$ are densely defined. It turns out that some s.a. Calogero Hamiltonians are oscillator type operators. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators.

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。

摘要：

英文摘要：

相关论文