Limits of regularizations for generalized function solutions to the Schrödinger equation with `square root of delta' initial value

DOI10.1007/s00041-017-9548-4zbMath1420.46035arXiv1612.09055OpenAlexW2563476322WikidataQ59607318 ScholiaQ59607318MaRDI QIDQ667670

Günther Hörmann

Publication date: 1 March 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.09055

zbMATH Keywords

invariant meanSchrödinger equationgeneralized functionsregularized solutions

Mathematics Subject Classification ID

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (5)

Schrödinger equation with singular position dependent mass ⋮ Study of nonlinear wave equation with singular data by using generalized fixed point ⋮ Generalised solutions to linear and non-linear Schrödinger-type equations with point defect: Colombeau and non-Colombeau regimes ⋮ Polymer quantum mechanics as a deformation quantization ⋮ Generalized solution to multidimensional cubic Schrödinger equation with delta potential

Cites Work

• The Cauchy problem for Schrödinger-type partial differential operators with generalized functions in the principal part and as data
• Hyperbolic systems with discontinuous coefficients: Generalized solutions and a transmission problem in acoustics
• Evolution systems for paraxial wave equations of Schrödinger-type with non-smooth coefficients
• Nonlinear Schrödinger equation with singular potential and initial data
• Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory
• Geodesics and geodesic deviation for impulsive gravitational waves
• The ultrarelativistic Reissner–Nordstro/m field in the Colombeau algebra
• Time of arrival from Bohmian flow
• A note on the Penrose junction conditions
• Generalized solutions to the cubic Schrödinger equation
• The use of generalized functions and distributions in general relativity
• PERTURBED SCHRÖDINGER EQUATION WITH SINGULAR POTENTIAL AND INITIAL DATA
• Generalized Summing Sequences and the Mean Ergodic Theorem
• Heat equation with singular potential and singular data
• Linear Functionals on Almost Periodic Functions
• Measure and integration theory
• Measure and integration theory. Transl. from the German by Robert B. Burckel
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