Mediterranean Journal of Modeling and Simulation
Volume 4, Numéro 1, Pages 060-072
2015-09-30
New Exact Bound States Solutions For (c.f.p.s.) Potential In The Case Of Non Commutative Three Dimensional Non Relativistic Quantum Mechanics
Authors : Maireche Abdelmadjid .
Abstract
We obtain here the modified bound-states solutions for central fraction power singular potential (C.F.P.S.) in noncommutative 3-dimensional non relativistic quantum mechanics (NC-3D NRQM). It has been observed that the commutative energy spectra was changed, and replaced degenerate new states, depending on four quantum numbers: j, l and sz=±1/2 corresponding to the two spins states of electron by (up and down) and the deformed Hamiltonian formed by two new operators: the first describes the spin-orbit interaction , while the second obtained Hamiltonian describes the modified Zeeman effect (containing ordinary Zeeman effect) in addition to the usual commutative Hamiltonian. We showed that the isotropic commutative Hamiltonian HCFPS will be in non commutative space anisotropic Hamiltonian HNC-CFPS.
Keywords
Schrödinger equation; Hydrogen atom; Star product; noncommutative space; Central fraction power singular potential.
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