The Quantum Arnold Transformation and the Ermakov-Pinney equation

Abstract

The previously introduced Quantum Arnold Transformation, a unitary operator mapping the solutions of the Schr\"odinger equation for time dependent quadratic Hamiltonians into the solutions for the free particle, is revised and some interesting extensions are introduced, providing in particular a generalization of the Ermakov-Pinney equation.Comment: 11 pages, 1 figure; to appear in Physica Script