No zero energy states for the supersymmetric x^2y^2 potential

Abstract

We show that the positive supersymmetric matrix-valued differential operator H={p_x}^2 + {p_y}^2 + x^2y^2 + xσ_3 + yσ_1 has no zero modes, i.e., H ψ= 0 implies ψ=0.