New Supercoherent States

TL;DR

This paper introduces a generalized class of supercoherent states for the supersymmetric quantum harmonic oscillator, analyzing their properties and uncertainties across different parameter regions.

Contribution

It extends supersymmetric coherent states by defining a 3-parameter family of annihilation operators and explicitly calculates their eigenstates.

Findings

Eigenstates explicitly calculated for key parameter regions

Uncertainty in position and momentum analyzed in detail

Identification of regions with saturated, bounded, and unbounded uncertainty

Abstract

This study generalizes the supersymmetric coherent states introduced by Aragone and Zypman in 1986. The Hamiltonian of the supersymmetric quantum harmonic oscillator leads to the definition of the generalized supersymmetric annihilation operators as a 3-parameter family. Their eigenstates are the generalized supercoherent states, which can be calculated explicitly for three relevant regions of parameter space. The uncertainty in position and momentum is discussed, with specific concentration on where the uncertainty is saturated, where it is bounded, and where it is unbounded.