sh(2/2) Superalgebra eigenstates and generalized supercoherent and supersqueezed states

TL;DR

This paper introduces superalgebra eigenstates for the $sh(2/2)$ superalgebra, deriving supercoherent and supersqueezed states, analyzing their properties, and constructing related superHermitian Hamiltonians with applications to supersymmetric quantum systems.

Contribution

It develops the concept of superalgebra eigenstates for $sh(2/2)$, deriving new classes of supercoherent and supersqueezed states, and applies these to construct novel superHermitian Hamiltonians.

Findings

Derived superalgebra eigenstates for $sh(2/2)$.

Constructed new supercoherent and supersqueezed states.

Built superHermitian Hamiltonians with supersymmetric properties.

Abstract

The superalgebra eigenstates (SAES) concept is introduced and then applied to find the SAES associated to the $sh(2/2)$ superalgebra, also known as Heisenberg--Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the $sh(2/2)$ SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the $osp(2/2) \sdir sh(2/2)$ superalgebra, where $osp(2/2)$ denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg--Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the superHermitian and $\eta$--pseudo--superHermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.