2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128173We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrodinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate involving the projections P+ and P- onto the positive and negative frequencies.Analysis of PDEs35J10; 35B65text