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

Abstract

Reciprocal Schrödinger equation for scattering matrix ∂S(ω, r)/ i∂ω = τ (ω, r)S(ω, 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 energymomentum 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.

Properties of Physical Systems: Transient Singularities on Borders and Surface Transitive Zones

“…with the projector 8) can be analyzed with the reciprocal equations of quantum dynamics [ 7 ] of the type (4.11) that contained the operator of interaction duration instead the Hamiltonian. It can lead to masses instability, etc.…”

“….10') For consideration of restrictions over admissible energy and/or momenta and corresponding projectors can be used the equation reciprocal to the Schrödinger equation: Hamiltonian the operator of interaction time duration is taken[ 7 ]. It leads to expansions analogical(4.3).…”

Quantum Electrodynamics of Multiphoton Processes: Laser Physics, Thermal Radiation and Astrophysics

“…its completely imaginary form corresponds to the duration of final state formation τ 2 described in [39]. If f b in (5.9) also, it is possible to assume that 2 |U | /v is about the momentum, which has been accumulated up by an electron at a starting from atom; then τ (p), in the full conformity with the Second Law, shows the duration of time necessary for accumulation of the momentum corresponding to kinetic energy of electron: τ n (p) = p n / b , (5.10) where p n ≈ [2m( − E n )] 1/2 at ionization within the state with the main quantum number n. Thus it can be assumed that b ∼ E n /a n = 1 2 (Zα) 2 · Ze 2 /(n 2 λ C ) 2 , i.e.…”

“…Thus, as against many known constructions (e.g., Muga et al [30]) durations of interaction are not entered ad hoc, artificially: they initially are present in QED (the general theory of the durations of interaction: Perel'man [38,39]). Just the existence of these factors give physical sense of the QED description of MPPs.…”

“…These functions can be considered as the self-functions of the reciprocal Schrödinger equation [39]: (1.4) i.e. the temporal functions corresponds to the operator ∂/i∂ω that can be generalized as the covariant operator ∂/i∂p μ , canonically conjugated to the energy-momentum operator i∂/∂x μ .…”