Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-05-16
J.Phys.A40:3539-3547,2007
Physics
High Energy Physics
High Energy Physics - Theory
Accepted in Journal of Physics A
Scientific paper
10.1088/1751-8113/40/13/015
We perform a 1-parameter family of self-adjoint extensions characterized by the parameter $\omega_0$. This allows us to get generic boundary conditions for the quantum oscillator on $N$ dimensional complex projective space($\mathbb{C}P^N$) and on its non-compact version i.e., Lobachewski space($\mathcal L_N$) in presence of constant magnetic field. As a result, we get a family of energy spectrums for the oscillator. In our formulation the already known result of this oscillator is also belong to the family. We have also obtained energy spectrum which preserve all the symmetry (full hidden symmetry and rotational symmetry) of the oscillator. The method of self-adjoint extensions have been discussed for conic oscillator in presence of constant magnetic field also.
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