Observability of a 1D Schrödinger Equation with Time-Varying Boundaries

Achache, Mahdi; Hoang, Duc-Trung

doi:10.1007/s10883-023-09640-6

Cited by 1 publication

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References 17 publications

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“…It will be the Dirichlet problem we are concerned with in the present paper. With all of this interest in how moving boundaries change the dynamics of quantum mechanical systems, there has also been a recent interest in both understanding observability in these systems [27] as well as using moving boundaries to control observables [28,29]. A generic treatment of the question of controlling observables via control of a moving boundary was carried out in [30].…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanics on time-varying space domains

Van Gorder

2023

Proc. R. Soc. A.

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The extension of quantum theory to time-varying space domains is often challenging, since domain evolution frequently results in non-autonomous and non-adiabatic evolution of corresponding wave function for a given quantum mechanical system. For generic domain evolution, we show that the evolution of the wave function is determined by the mixing of spatial modes or bound states, and this is the instigator for non-adiabatic wave function evolution. For some applications, it is desirable to retain adiabaticity of the wave function and with knowledge of how domain evolution causes loss of adiabaticity, we construct a control potential—comprising a harmonic term and a volume expansion/contraction term—which may be used to counteract this feature of domain evolution, thereby preserving wave function adiabaticity throughout the time evolution of the space domain. Examples of quantum mechanical systems on time-varying space domains are used to illustrate the theory, including analogues of classical examples such as the hydrogen atom and quantum harmonic oscillator on unbounded stretched space and a particle in a stretched and translated box. We also discuss how to combine our approach with numerical simulations, using the compressed hydrogen atom confined within an evolving sphere to demonstrate the method.

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Section: Introductionmentioning

confidence: 99%

Quantum mechanics on time-varying space domains

Van Gorder

2023

Proc. R. Soc. A.

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Observability of a 1D Schrödinger Equation with Time-Varying Boundaries

Cited by 1 publication

References 17 publications

Quantum mechanics on time-varying space domains

Quantum mechanics on time-varying space domains

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