Abstract
A truncated basis is employed to analyze the influence of the point interaction on the eigenvalues and eigenfunctions in quantum billiards. The point interaction is numerically confirmed to cause the shift in the eigenvalue that leads the original eigenfunctions to be superposed to form the new eigenfunction. The amplitude and nodal-line patterns of the eigenfunctions are found to vary significantly with the coupling strength. It is further verified that the point-driven Chladni plates can be employed to analogously manifest the noticeable dependence of the nodal-line pattern on the coupling strength. More importantly, the dispersion relation between the frequency and the wave number for the flexural wave can be precisely determined in the process of utilizing the point interaction to model the modern Chladni plates.
Highlights
In this work,Model we study of point interaction on the resonant modes in
We basis to explore the influence of theofpoint point interaction the eigenvalues and eigenfunctions in quantum billiards
We have numernumerically found shift in the eigenvalue the eigenfunction ofinteraction the point ically found that thethat shiftthe in the eigenvalue leads the leads eigenfunction of the point interaction to be the superposition of the unperturbed eigenfunctions
Summary
We systematically verify that the perceptible of the nodal-line pattern on the coupling strength can be analogously manifested from th point-driven Chladni plates. The explorations regarding to the point interaction almost all focus on the variation model is believed to be pedagogically beneficial to understanding the point in of eigenvalues, and rarely on the structure of eigenfunctions It is scientifically important quantum practically useful for measuring the acoustic prop toteraction verify theininfluence of systems the point but interaction on the pattern formation of eigenfunctions erties of plates. The issue offlexural quantum billiards is associated with the proposed model is believed to be pedagogically beneficial to understanding the point interaction in quantum systems and practically useful for measuring the acoustic properties of plates
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