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 + x\sigma_3 + y\sigma_1 has no zero modes, i.e., H \psi = 0 implies \psi =0.