A Criterion for the Existence of the Complete Wave Operators in the Theory of Scattering with Two Spaces

1971 ◽  
pp. 17-21
Author(s):  
M. Sh. Birman
Keyword(s):  
Wave Operators

scholarly journals Spherical wave operators and the translation formulas

1988 ◽  
Vol 36 (8) ◽  
pp. 1078-1087 ◽  
Author(s):  
R.C. Wittmann
Keyword(s):  
Spherical Wave ◽  
Wave Operators

scholarly journals Electromagnetic Gauge Choice for Scattering of Schrödinger Particle

2019 ◽  
Vol 20 (11) ◽  
pp. 3633-3650
Author(s):  
Andrzej Herdegen
Keyword(s):  
Asymptotic Behavior ◽  
External Electromagnetic Field ◽  
Asymptotic Completeness ◽  
Free Evolution ◽  
Wave Operators ◽  
Radiation Fields ◽  
Mechanical Evolution ◽  
Scattering Wave ◽  
Free Fields

Abstract We consider a Schrödinger particle placed in an external electromagnetic field of the form typical for scattering settings in the field theory: $$F=F^\mathrm {ret}+F^\mathrm {in}=F^\mathrm {adv}+F^\mathrm {out}$$ F = F ret + F in = F adv + F out , where the current producing $$F^{\mathrm {ret}/\mathrm {adv}}$$ F ret / adv has the past and future asymptotes homogeneous of degree $$-3$$ - 3 , and the free fields $$F^{\mathrm {in}/\mathrm {out}}$$ F in / out are radiation fields produced by currents with similar asymptotic behavior. We show that with appropriate choice of electromagnetic gauge the particle has ‘in’ and ‘out’ states reached with no further modification of the asymptotic dynamics. We use a special quantum mechanical evolution ‘picture’ in which the free evolution operator has well-defined limits for $$t\rightarrow \pm \infty $$ t → ± ∞ , and thus the scattering wave operators do not need the free evolution counteraction. The existence of wave operators in this setting is established, but the proof of asymptotic completeness is not complete: more precise characterization of the asymptotic behavior of the particle for $$|\mathbf {x}|=|t|$$ | x | = | t | would be needed.

scholarly journals New Formulae for the Wave Operators for a Rank One Interaction

2010 ◽  
Vol 66 (2) ◽  
pp. 283-292 ◽  
Author(s):  
Serge Richard ◽  
Rafael Tiedra de Aldecoa
Keyword(s):  
Wave Operators ◽  
Rank One

On convergence to the møller wave operators

1958 ◽  
Vol 9 (4) ◽  
pp. 731-733 ◽  
Author(s):  
M. N. Hack
Keyword(s):  
Wave Operators
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