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We generalize the Lewis-Riesenfeld technique of solving the time-dependentSchrodinger equation to cases where the invariant has continuous eigenvalues.An explicit formula for a generalized Lewis-Riesenfeld phase is derived interms of the eigenstates of the invariant. As an illustration the generalizedphase is calculated for a particle in a time-dependent linear potential.

Solutions to the time-dependent Schrodinger equation in the continuous spectrum case