Observability for Schrödinger equations with quadratic Hamiltonians

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Alden Marie Seaburg Waters

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Original languageEnglish
Article number12
JournalPartial Differential Equations and Applications
Volume4
Issue number2
Early online date8 Mar 2023
Publication statusPublished - Apr 2023

Abstract

We consider time dependent harmonic oscillators and construct a parametrix to the corresponding Schrödinger equation using Gaussian wavepackets. This parametrix of Gaussian wavepackets is precise and tractable. Using this parametrix we prove L^2 and L^2-L^{\infty} observability estimates on unbounded domains for a restricted class of initial data. This data includes a class of compactly supported piecewise C^1 functions which have been extended from characteristic functions. Initial data of this form which has the bulk of its mass away from Omega^c, a connected bounded domain, is observable, but data centered over Omega must be very nearly a single Gaussian to be observable. We also give counterexamples to established principles for the simple harmonic oscillator in the case of certain time dependent harmonic oscillators.

Keywords

    Control theory, Observability, Schrödinger equations

ASJC Scopus subject areas

Cite this

Observability for Schrödinger equations with quadratic Hamiltonians. / Waters, Alden Marie Seaburg.
In: Partial Differential Equations and Applications, Vol. 4, No. 2, 12, 04.2023.

Research output: Contribution to journal › Article › Research › peer review

Waters, AMS 2023, 'Observability for Schrödinger equations with quadratic Hamiltonians', Partial Differential Equations and Applications, vol. 4, no. 2, 12. https://doi.org/10.1007/s42985-023-00229-z
Waters, A. M. S. (2023). Observability for Schrödinger equations with quadratic Hamiltonians. Partial Differential Equations and Applications, 4(2), Article 12. https://doi.org/10.1007/s42985-023-00229-z
Waters AMS. Observability for Schrödinger equations with quadratic Hamiltonians. Partial Differential Equations and Applications. 2023 Apr;4(2):12. Epub 2023 Mar 8. doi: 10.1007/s42985-023-00229-z
Waters, Alden Marie Seaburg. / Observability for Schrödinger equations with quadratic Hamiltonians. In: Partial Differential Equations and Applications. 2023 ; Vol. 4, No. 2.
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