Uncertainties of coherent states for a generalized supersymmetric annihilation operator

Abstract

This study presents supersymmetric coherent states that are eigenstates of a general four-parameter family of annihilation operators. The elements of this family are defined as operators in Fock space that transform a subspace of a definite number of particles into a subspace with one particle removed. The emphasis is on classifying parameter space in various regions according to the uncertainty bounds of the corresponding coherent states. Specifically, the uncertainty in position-momentum is analyzed, with specific focus on characterizing regions of minimum uncertainty states, regions where the uncertainties are bounded from above, and where they grow unbound.