R. de Lima Rodrigues

A class of double-well like potentials in 1 + 1 dimensions via SUSY QM

The connection between the soliton solutions for potentials in 1 + 1 dimensions and supersymmetry in the context of non-relativistic quantum mechanics is explored. Examining the equivalence between a supersymmetric partner and the stability equation of the model, which is a Schrodinger-like equation for the normal modes, we construct two new supersymmetric partners, which leads us to a new class of isospectral potentials in quantum mechanics and a new class of potential nonlinear models in bidimensional spacetime. We show that such new potentials in 1 + 1 dimensions are double-well like potentials.

A SUSY formulation àla Witten for the SUSY isotonic oscillator canonical supercoherent states

We extend Wittens supersymmetry (SUSY) formulation for Hamiltonian systems to a system of annihilation operator eigenvalue equations associated with the SUSY isotonic oscillator, which, as we show, define SUSY canonical supercoherent states containing mixtures of both pure bosonic and pure fermionic counterparts. Specifically, a graded Lie algebra structure analogous to Wittens SUSY quantum mechanical algebra is realized in which only annihilation operators participate, all expressed in terms of the Wigner annihilation operator of a related super-Wigner oscillator system.

A representation of the Virasoro algebra via Wigner-Heisenberg algebraic technique to bosonic systems

Using the Wigner-Heisenberg algebra for bosonic systems in connection with oscillators we find a new representation for the Virasoro algebra.

q-DEFORMED KINK SOLUTIONS

The q-deformed kink of the λϕ4-model is obtained via the normalizable ground state eigenfunction of a fluctuation operator associated with the q-deformed hyperbolic functions. From such a bosonic zero-mode the q-deformed potential in 1+1 dimensions is found, and we show that the q-deformed kink solution is a kink displaced away from the origin.