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International Journal of Theoretical Physics

, Volume 47, Issue 2, pp 468–491 | Cite as

Reciprocal Schrödinger Equation: Durations of Delay and Formation of States in Scattering Processes

  • Mark E. Perel’man
Article

Abstract

Reciprocal Schrödinger equation for scattering matrix \(\partial S(\omega,\mathbf{r})/i\partial\omega= \hat{\tau}(\omega,\mathbf{r})S(\omega,\mathbf{r})\) determines temporal function, its real part presents the Wigner–Smith duration of delay and imaginary part describes the duration of resulted (dressed) state formation. “Deduction” of this equation is executed by the Legendre transformation of classical action function with subsequent transition to quantum description and, in the covariant form, by a temporal variant of the Bogoliubov variational method. Temporal functions are expressed via propagators of fields, they are formally equivalent to adding a photon line of zero energy-momentum to the Feynman graphs. As an apparent example they can be clearly interpreted in the oscillator model via polarization and conductivity of medium. It is shown that the adiabatic hypothesis in scattering theory represents an implicit account of temporal parameters. By these functions are described some renormalization procedures, their physical sense is refined, etc.

Keywords

Temporal functions Scattering Dressing Sense of renormalization 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Racah Institute of PhysicsHebrew UniversityJerusalemIsrael

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