Schrödinger equation for convex plane polygons: A tiling method for the derivation of eigenvalues and eigenfunctions

DOI10.1063/1.529172zbMath0751.58027OpenAlexW2024882584MaRDI QIDQ3987377

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Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.529172

zbMATH Keywords

plane waveseigenvalueseigenfunctionsSchrödinger equationfree particleconvex polygonal domain

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Ergodic theorems, spectral theory, Markov operators (37A30) Convex sets in (2) dimensions (including convex curves) (52A10) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (6)

Nodal-surface conjectures for the convex quantum billiard ⋮ Influence of impurity on binding energy and optical properties of lens shaped quantum dots: finite element method and Arnoldi algorithm ⋮ Nodal and other properties of the second eigenfunction of the Laplacian in the plane ⋮ Rings, quadratic forms, and complete degeneracy for a subclass of highly overmoded rectangular waveguides ⋮ Schrödinger equation for convex plane polygons. II. A no-go theorem for plane waves representation of solutions ⋮ Electron–phonon interaction influence on optical properties of parallelogram quantum wires

Cites Work

• Non-periodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons
• Pseudointegrable systems in classical and quantum mechanics
• Analytically solvable dynamical systems which are not integrable
• Ergodicity of billiard flows and quadratic differentials
• Spectres et groupes cristallographiques. I: Domaines euclidiens. (Spectra and crystallographic groups. I: Euclidean domains)
• Topological transitivity of billiards in polygons
• Diabolical points in the spectra of triangles
• Eigenvalues of the Laplacian in Two Dimensions
• Solution of the Schrödinger equation for a particle in an equilateral triangle
• Periods of Multiple Reflecting Geodesics and Inverse Spectral Results
• SIMPLE INTEGRABLE SYSTEMS, AND LIE ALGEBRAS
• The Eigenvalues of an Equilateral Triangle

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