Two-dimensional Helmholtz equation with zero Dirichlet boundary condition on a circle: Analytic results for boundary deformation, the transition disk-lens

DOI10.1063/1.5093812zbMath1421.81035OpenAlexW2964591303MaRDI QIDQ5234044

E. de Prunelé

Publication date: 9 September 2019

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.5093812

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) (2)-body potential quantum scattering theory (81U05) Boundary value problems for linear higher-order PDEs (35G15) Formal methods and deformations in algebraic geometry (14D15) Green's functions for elliptic equations (35J08)

Cites Work

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• Dirichlet problems on varying domains.
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• Solvable quantum mechanical model in two-dimensional space
• Mathematical Analysis of Evolution, Information, and Complexity
• On the solution of the two-dimensional Helmholtz equation
• Eigenvalues of the Laplacian in Two Dimensions
• Bound states for two dimensional Schrödinger equation with anisotropic interactions localized on a circle

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