Abstract
The two dimensional quantum dipole springs in background uniform electric and magnetic fields are first studied in the conventional commutative coordinate space, leading to rigorous results. Then, the model is studied in the framework of the noncommutative (NC) phase space. The NC Hamiltonian and angular momentum do not commute any more in this space. By the means of the su(1,1) symmetry and the similarity transformation, exact solutions are obtained for both the NC angular momentum and the NC Hamiltonian.
Highlights
The discovery of new fundamental interactions and the development of quantum field theory have opened the way to many research works
We have studied a generalization of the two dimensional quantum dipole coupled to external uniform electric and magnetic background fields
The quantum dipole is studied in the NC phase space
Summary
The discovery of new fundamental interactions and the development of quantum field theory have opened the way to many research works. We extend and study in the NC phase space with an uniform background magnetic field, the model describing a system of two nonrelativistic charged particles of identical mass, of opposite charges and linked by a spring through an harmonic potential. We extend and study in the NC phase space with an uniform background magnetic field, the model describing a system of two nonrelativistic charged particles of identical mass, of opposite charges and linked by a spring through an harmonic potential1 This extension constists of considering an electric field in addition to the magnetic field and a confining potential. This lights the way for us, where we deal with the study of the system in NC phase space.
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