Numerical Solutions of the Spectral Problem for Arbitrary Self-Adjoint Extensions of the One-Dimensional Schrödinger Equation

DOI10.1137/110856800zbMath1279.65093arXiv1103.5588OpenAlexW1978918983MaRDI QIDQ2840397

Juan Manuel Pérez-Pardo, Alberto Ibort

Publication date: 18 July 2013

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.5588

zbMATH Keywords

algorithm stability convergence finite element method numerical examples eigenvalue problem Schrödinger operator boundary element methods spectral problem

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) Applications of boundary value problems involving ordinary differential equations (34B60) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (8)

Boundary dynamics and topology change in quantum mechanics ⋮ Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions ⋮ On Global Approximate Controllability of a Quantum Particle in a Box by Moving Walls ⋮ On self-adjoint extensions and symmetries in quantum mechanics ⋮ Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary ⋮ Representation of non-semibounded quadratic forms and orthogonal additivity ⋮ Self-adjoint extensions of the Laplace-Beltrami operator and unitaries at the boundary ⋮ Near-Dirichlet quantum dynamics for a \(p^3\)-corrected particle on an interval

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