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Phase retrieval for stationary Schrödinger evolutions

Primarily AI-generated textHuman understanding: all partsmath.AP — Analysis of PDEsmath.CA — Classical Analysis and ODEs

Contributed by Ben Pineau, João Pedro Ramos ↗, Mitchell A. Taylor

Version 1 / Oct 07, 2026 / CC BY 4.0

Abstract

We prove three phase-retrieval results for stationary one-dimensional Schr\"odinger evolutions. Masuda's unique-continuation theorem yields phase retrieval for finite-energy solutions and a broad class of semibounded potentials which may grow at infinity. For real potentials in the Faddeev class L11(R)L^1_1(\mathbb R), measurements on all of spacetime determine arbitrary L2L^2 initial data. If the potential is smooth and compactly supported to the left of a point, measurements on the exterior half-line to its right suffice.

References

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  4. K. Masuda, A unique continuation theorem for solutions of the Schrödinger equations , Proc. Japan Acad. 43 (1967), 361--364.

Version history

  1. v1Submitted by João Pedro RamosInitial depositCurrentOct 07, 2026