Wave operators for the Schr�dinger equation with strongly singular short-range potentials

1977 ◽  
Vol 1 (6) ◽  
pp. 457-461 ◽  
Author(s):  
Yu. A. Semenov
Keyword(s):  
Short Range ◽  
Dinger Equation ◽  
Wave Operators

Modified wave operators for the derivative nonlinear Schr�dinger equation

1994 ◽  
Vol 298 (1) ◽  
pp. 557-576 ◽  
Author(s):  
Nakao Hayashi ◽  
Tohru Ozawa
Keyword(s):  
Dinger Equation ◽  
Wave Operators

On the Schrödinger equation with time-dependent electric fields

1984 ◽  
Vol 96 (1-2) ◽  
pp. 117-134 ◽  
Author(s):  
Rafael José Iório ◽  
Dan Marchesin
Keyword(s):  
Schrödinger Equation ◽  
Electric Fields ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Short Range ◽  
Bound States ◽  
Time Dependent ◽  
Uniqueness Of Solutions ◽  
Wave Operators

SynopsisWe prove existence and uniqueness of solutions of i(∂ψ/∂t) = (−Δ+x1g(t)+q(x))ψ, ψ(x, s) = ψs (x) in ℝ3 for potentials q(x) including the Coulomb case. Existence and completeness of the wave operators is established for g(t) periodic with zero mean and q(x) short-range, smooth in the x1 direction. We characterize scattering and bound states in terms of the period operator.

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