Coulomb problem in non-commutative quantum mechanics - Exact solution

Autor:	Gáliková, Veronika, Prešnajder, Peter
Rok vydání:	2011
Předmět:	Mathematical Physics High Energy Physics - Theory
Druh dokumentu:	Working Paper
Popis:	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 $\hat{\psi}$ 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 $E^\lambda_n$ and the corresponding eigenstates $\hat{\psi}^\lambda_{njm}$. The Coulomb scattering problem in $\hat{\bf R}^3_0$ is under study. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1112.4643 Zobrazit plný text záznamu View this record from Arxiv