About: Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1007/s10773-013-1640-1
Description	It is known that the Heisenberg and Robertson-Schrodinger uncertainty relations can be replaced by sharper uncertainty relations in which the %22classical%22 (depending on the gradient of the phase of the wave function) and %22quantum%22 (depending on the gradient of the envelope of the wave function) parts of the variances <(Delta x)^2> and a<(Delta p)(2)> are separated. In this paper, three types of uncertainty relations for a different number of classical parts (2, 1 or 0) with different time behaviour of their left-hand and right-hand sides are discussed. For the Gaussian wave packet and two classical parts, the left-hand side of the corresponding relations increases for t -> infinity as t ^2 and is much larger than hbar^2/4. For one classical part, the left-hand side of the corresponding relation goes to the right-hand side equal to hbar^2/4. For no classical part, both the right-hand and left-hand sides of the corresponding relation go quickly to zero. Therefore, the well-known limitations following from the usual uncertainty relations can be overcome in the corresponding measurements. It is known that the Heisenberg and Robertson-Schrodinger uncertainty relations can be replaced by sharper uncertainty relations in which the %22classical%22 (depending on the gradient of the phase of the wave function) and %22quantum%22 (depending on the gradient of the envelope of the wave function) parts of the variances <(Delta x)^2> and a<(Delta p)(2)> are separated. In this paper, three types of uncertainty relations for a different number of classical parts (2, 1 or 0) with different time behaviour of their left-hand and right-hand sides are discussed. For the Gaussian wave packet and two classical parts, the left-hand side of the corresponding relations increases for t -> infinity as t ^2 and is much larger than hbar^2/4. For one classical part, the left-hand side of the corresponding relation goes to the right-hand side equal to hbar^2/4. For no classical part, both the right-hand and left-hand sides of the corresponding relation go quickly to zero. Therefore, the well-known limitations following from the usual uncertainty relations can be overcome in the corresponding measurements. (en)
Title	Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations (en)
skos:prefLabel	Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations (en)
skos:notation	RIV/00216208:11320/13:10173454!RIV14-MSM-11320___
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	10
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Skála, Lubomír
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	80799
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10173454
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Three types of uncertainty relations; Uncertainty relations; Quantum mechanics (en)
http://linked.open.../riv/klicoveSlovo	Three types of uncertainty relations Uncertainty relations Quantum mechanics
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[8FC5E58BFC30]
http://linked.open...i/riv/nazevZdroje	International Journal of Theoretical Physics
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	52
http://linked.open...iv/tvurceVysledku	Skála, Lubomír
http://linked.open...ain/vavai/riv/wos	000324099800004
issn	0020-7748
number of pages	12 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s10773-013-1640-1
http://localhost/t...ganizacniJednotka	11320

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