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

TL;DR

This paper introduces a new class of spin coherent states using monopole harmonics on the Riemann sphere, applies them to the Kravchuk oscillator, and develops a Bargmann-type representation for these states.

Contribution

It constructs generalized spin coherent states with monopole harmonic labels and applies them to the Kravchuk oscillator, providing explicit wave functions and a new Bargmann-type transform.

Findings

Verified Klauder minimum properties for the new states

Derived explicit wave functions for the Kravchuk oscillator

Identified lowest level states as Klauder-Perelomov coherent states

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)