scholarly journals Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell–Schrödinger equations

2012 ◽  
Vol 263 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Takeshi Wada
Keyword(s):  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Smoothing Effects ◽  
Electro Magnetic ◽  
Magnetic Potentials

SCHRÖDINGER EQUATIONS WITH TIME-DEPENDENT UNBOUNDED SINGULAR POTENTIALS

2011 ◽  
Vol 23 (08) ◽  
pp. 823-838 ◽  
Author(s):  
KENJI YAJIMA
Keyword(s):  
Evolution Equations ◽  
Schrödinger Operators ◽  
Time Variable ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Singular Potentials ◽  
Spatial Infinity ◽  
Abstract Theorem ◽  
Magnetic Potentials

We consider time-dependent perturbations by unbounded potentials of Schrödinger operators with scalar and magnetic potentials which are almost critical for the selfadjointness. We show that the corresponding time-dependent Schrödinger equations generate a unique unitary propagator if perturbations of scalar and magnetic potentials are differentiable with respect to the time variable and they increase at the spatial infinity at most quadratically and at most linearly, respectively, where both have mild local singularities. We use time-dependent gauge transforms and apply Kato's abstract theorem on evolution equations.

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