SCHRÖDINGER EQUATIONS WITH TIME-DEPENDENT UNBOUNDED SINGULAR POTENTIALS

DOI10.1142/S0129055X11004436zbMath1229.35226OpenAlexW2045820994MaRDI QIDQ3098866

Kenji Yajima

Publication date: 18 November 2011

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

Full work available at URL: https://doi.org/10.1142/s0129055x11004436

zbMATH Keywords

initial value problempropagatorstime-dependent Schrödinger equations

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Perturbation theories for operators and differential equations in quantum theory (81Q15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (9)

Improved energy estimates for a class of time-dependent perturbed Hamiltonians ⋮ Existence and regularity of propagators for multi-particle Schrödinger equations in external fields ⋮ Schrödinger equations with time-dependent strong magnetic fields ⋮ Notes on the Cauchy problem for the self-adjoint and non-self-adjoint Schrödinger equations with polynomially growing potentials ⋮ Well-posedness of non-autonomous linear evolution equations in uniformly convex spaces ⋮ Unitary propagators for N-body Schrödinger equations in external field ⋮ An evolution equation approach to the Klein-Gordon operator on curved spacetime ⋮ Smoothing estimates for the Schrödinger equation with unbounded potentials ⋮ Electromagnetic gauge choice for scattering of Schrödinger particle

Cites Work

• Smoothness and non-smoothness of the fundamental solution of time dependent Schrödinger equations
• Essential self-adjointness of the Schrödinger operators with magnetic fields diverging at infinity
• Existence of solutions for Schrödinger evolution equations
• Schrödinger evolution equations with magnetic fields
• Smoothness of solutions for Schrödinger equations with unbounded potentials
• Stationary scattering theory for time-dependent Hamiltonians
• Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control
• Schrödinger operators with singular magnetic vector potentials
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