Spin coherent states with monopole harmonics on the Riemann sphere for the Kravchuk oscillator

Abstract

We consider a class of generalized spin coherent states by choosing the labeling coefficients to be monopole harmonics.The latters are L2 eigenstates of the mth spherical Landau level on the Riemann sphere with m in Z+. We verify that the Klauder minimum properties for these states to be considered as coherent states are satisfied. We particularize them for the case of the Kravchuk oscillator and we obtain explicite expression for their wave functions.The associated coherent states transforms provide us with a Bargmann-type representation for the states of the oscillator Hilbert space. For the lowest level m = 0 indexing monopole harmonics, we identify the obtained coherent states to be those of Klauder-Perelomov type which were constructed in Ref.J. Math. Phys. 48, 112106 (2007)