Uncertainty Principle of Morgan type and Schr\"odinger Evolutions
L. Escauriaza, C. E. Kenig, G. Ponce, and L. Vega
TL;DR
This paper establishes unique continuation properties for solutions of time-dependent Schr"odinger equations, including Morgan-type uncertainty principles for free solutions and insights into concentration profiles of semi-linear solutions.
Contribution
It introduces new unique continuation results for Schr"odinger equations with time-dependent potentials and extends Morgan-type uncertainty principles to this context.
Findings
Unique continuation for Schr"odinger solutions with time-dependent potentials
Morgan-type uncertainty principles for free solutions
Characterization of concentration profiles in semi-linear Schr"odinger equations
Abstract
We prove unique continuation properties for solutions of evolution Schr\"odinger equation with time dependent potentials. In the case of the free solution these correspond to uncertainly principles referred to as being of Morgan type. As an application of our method we also obtain results concerning the possible concentration profiles of solutions of semi-linear Schr\"odinger equations.
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