Explicit Phase Space Transformations and Their Application in Noncommutative Quantum Mechanics - Hung, Nguyen Quang; Tuan, Do Quoc (VNU Journal of Science: Mathematics - Physics; Vol 31 No 2, 2015)
We study a problem of transformations mapping noncommutative phase spaces into commutative ones. We find a simple way to obtain explicit formulas of such transformations in 3D and indicate matrix equations for numerical computation in higher dimensions. Then we use these formulas to calculate the energy levels of the hydrogen-like atom with six noncommutative parameters. We also find and prove new relations between the hydrogen eigenfunctions corresponding to the n -th energy level.   Keywords: Noncommutativity, noncommutative quantum mechanics, Hydrogen-like atom. PACS numbers: 11.10.Nx, 02.40.Gh, 31.15.-p, 03.65.-w, 03.65.Fd.