arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1702.05049math-phmath.MPquant-ph
收藏

由双正交集定义的Hamilton算子

Hamiltonians defined by biorthogonal sets

Fabio Bagarello, Giorgia Bellomonte

备注：
in press in Journal of Physics A
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

在最近的一些论文中，双正交Riesz基的研究找到了新的动力，因为它们与伪厄米量子力学的联系，其中涉及的物理系统的哈密顿量，这是不是自伴，但仍然可能有实点谱。此外，它们的特征向量可以形成定义模型的希尔伯特空间的Riesz基，而不一定是标准正交基。这些Riesz基允许哈密顿量的分解，正如已经讨论过的一些以前的论文。然而，在许多物理模型中，我们不得不处理的不是o. n。基或Riesz基，但只是双正交集。在这里，我们考虑更一般的概念，$\mathcal{G}$ -拟基，我们展示了一系列的条件下，定义的非自伴哈密顿量与纯点实谱仍然是可能的。

英文摘要：

In some recent papers, the studies on biorthogonal Riesz bases has found a renewed motivation because of their connection with pseudo-hermitian Quantum Mechanics, which deals with physical systems described by Hamiltonians which are not self-adjoint but still may have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed is some previous papers. However, in many physical models, one has to deal not with o.n. bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of $\mathcal{G}$-quasi basis and we show a series of conditions under which a definition of non self-adjoint Hamiltonian with purely point real spectra is still possible.

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。

↑