  We study a two dimensional system of electrons with Rashba coupling in the
constant magnetic field $B$ and confining potential. We algebraically
diagonalize the corresponding Hamiltonian to end up with the solutions of the
energy spectrum. In terms of two kinds of operator we construct two symmetries
and discuss the filling of the shells with electrons for strong and weak $B$.
Subsequently, we show that our system is sharing some common features with
quantum optics where the exact operator solutions for the basics
Jaynes-Cummings variables are derived from our results. An interesting limit is
studied and the corresponding quantum dynamics is recovered.
