arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新，休息一下吧，周末愉快~~
arXiv 1112.4643math-phhep-thmath.MP
收藏

非对易量子力学中的库仑问题--精确解

Coulomb problem in non-commutative quantum mechanics - Exact solution

Veronika Gáliková, Peter Prešnajder

备注：
18 pages
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们研究了氢原子量子力学中空间非对易性的后果。我们引入旋转不变的非对易空间$\hat{\bf R}^3_0$ -一个类似的氢原子（$H$ -原子）的位形空间${\bf R}^3_0\,=\, {\bf R}^3\setminus \{0\}$。空间$\hat{\bf R}^3_0$由实现为辅助（Fock）空间${\cal F}$中的算子的非交换坐标生成。在${\cal F}$中引入适当加权的Hilbert-Schmidt算子所形成的波函数$\hatψ$的Hilbert空间$\hat{\cal{H}}$.最后，我们在$\hat{\bf R}^3_0$中定义了一个类似的$H$原子哈密顿量，并明确地确定了束缚态能量$E^λ_n$和相应的本征态$\hatψ^λ_{njm}$ .研究了$\hat{\bf R}^3_0$中的库仑散射问题。

英文摘要：

We investigate consequences of space non-commutativity in quantum mechanics of the hydrogen atom. We introduce rotationally invariant noncommutative space $\hat{\bf R}^3_0$ - an analog of the hydrogen atom ($H$-atom) configuration space ${\bf R}^3_0\,=\, {\bf R}^3\setminus \{0\}$. The space $\hat{\bf R}^3_0$ is generated by noncommutative coordinates realized as operators in an auxiliary (Fock) space ${\cal F}$. We introduce the Hilbert space $\hat{\cal{H}}$ of wave functions $\hatψ$ formed by properly weighted Hilbert-Schmidt operators in ${\cal F}$. Finally, we define an analog of the $H$-atom Hamiltonian in $\hat{\bf R}^3_0$ and explicitly determine the bound state energies $E^λ_n$ and the corresponding eigenstates $\hatψ^λ_{njm}$. The Coulomb scattering problem in $\hat{\bf R}^3_0$ is under study.

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。

↑