The quantum oscillator on complex projective space (Lobachewski space) in a constant magnetic field and the issue of generic boundary conditions

Pulak Ranjan Giri
2007 Journal of Physics A: Mathematical and Theoretical  
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
more » ... or 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.
doi:10.1088/1751-8113/40/13/015 fatcat:ehq7hw32i5djvmesag5xcc54wa