Remark on quantum mechanics with N=2N=2 Schrödinger supersymmetry

A unitary transformation which relates a many-body quantum mechanics with N=2N=2 Schrödinger supersymmetry to a set of decoupled superparticles is proposed. The simplification in dynamics is achieved at a price of a nonlocal realization of the full N=2N=2 Schrödinger superalgebra in a Hilbert space. The transformation is shown to be universal and applicable to conformal many-body models confined in a harmonic trap.