dorsal/arxiv
View SchemaReciprocal Schr\"{o}dinger Equation: Durations of Delay and of Final States Formation in Processes of Scattering
| Authors | Mark E. Perel'man |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0311169 |
| URL | https://arxiv.org/abs/quant-ph/0311169 |
Abstract
The reciprocal Schr\"{o}dinger equation $\partial S(\omega ,{\bf r}% )/i\partial \omega =\hat{\tau}(\omega ,{\bf r}) S(\omega ,{\bf r})$ for $S$-matrix with temporal operator instead the Hamiltonian is established via the Legendre transformation of classical action function. Corresponding temporal functions are expressed via propagators of interacting fields. Their real parts $\tau_{1}$are equivalent to the Wigner-Smith delay durations at process of scattering and imaginary parts $\tau_{2}$ express the duration of final states formation (dressing). As an apparent example, they can be clearly interpreted in the oscillator model via polarization ($% \tau_{1}$) and conductivity ($\tau_{2}$) of medium. The $\tau $-functions are interconnected by the dispersion relations of Kramers-Kr\"{o}nig type. From them follows, in particular, that $\tau_{2}$ is twice bigger than the uncertainty value and thereby is measurable; it must be negative at some tunnel transitions and thus can explain the observed superluminal transfer of excitations at near field intervals (M.E.Perel'man. In: arXiv. physics/0309123). The covariant generalizations of reciprocal equation clarifies the adiabatic hypothesis of scattering theory as the requirement: $% \tau_{2}\to 0$ at infinity future and elucidate the physical sense of some renormalization procedures.
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"abstract": "The reciprocal Schr\\\"{o}dinger equation $\\partial S(\\omega ,{\\bf r}%\n)/i\\partial \\omega =\\hat{\\tau}(\\omega ,{\\bf r}) S(\\omega ,{\\bf r})$ for\n$S$-matrix with temporal operator instead the Hamiltonian is established via\nthe Legendre transformation of classical action function. Corresponding\ntemporal functions are expressed via propagators of interacting fields. Their\nreal parts $\\tau_{1}$are equivalent to the Wigner-Smith delay durations at\nprocess of scattering and imaginary parts $\\tau_{2}$ express the duration of\nfinal states formation (dressing). As an apparent example, they can be clearly\ninterpreted in the oscillator model via polarization ($% \\tau_{1}$) and\nconductivity ($\\tau_{2}$) of medium. The $\\tau $-functions are interconnected\nby the dispersion relations of Kramers-Kr\\\"{o}nig type. From them follows, in\nparticular, that $\\tau_{2}$ is twice bigger than the uncertainty value and\nthereby is measurable; it must be negative at some tunnel transitions and thus\ncan explain the observed superluminal transfer of excitations at near field\nintervals (M.E.Perel\u0027man. In: arXiv. physics/0309123). The covariant\ngeneralizations of reciprocal equation clarifies the adiabatic hypothesis of\nscattering theory as the requirement: $% \\tau_{2}\\to 0$ at infinity future and\nelucidate the physical sense of some renormalization procedures.",
"arxiv_id": "quant-ph/0311169",
"authors": [
"Mark E. Perel\u0027man"
],
"categories": [
"quant-ph"
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"title": "Reciprocal Schr\\\"{o}dinger Equation: Durations of Delay and of Final States Formation in Processes of Scattering",
"url": "https://arxiv.org/abs/quant-ph/0311169"
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