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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F13%3A10173454%21RIV14-MSM-11320___
rdf:type
skos:Concept n7:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1007/s10773-013-1640-1
dcterms: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.
dcterms:title
Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations
skos:prefLabel
Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations Internal Structure of the Heisenberg and Robertson-Schrodinger Uncertainty Relations
skos:notation
RIV/00216208:11320/13:10173454!RIV14-MSM-11320___
n7:predkladatel
n8:orjk%3A11320
n3:aktivita
n18:I
n3:aktivity
I
n3:cisloPeriodika
10
n3:dodaniDat
n15:2014
n3:domaciTvurceVysledku
n5:4127870
n3:druhVysledku
n20:J
n3:duvernostUdaju
n6:S
n3:entitaPredkladatele
n14:predkladatel
n3:idSjednocenehoVysledku
80799
n3:idVysledku
RIV/00216208:11320/13:10173454
n3:jazykVysledku
n17:eng
n3:klicovaSlova
Three types of uncertainty relations; Uncertainty relations; Quantum mechanics
n3:klicoveSlovo
n4:Uncertainty%20relations n4:Quantum%20mechanics n4:Three%20types%20of%20uncertainty%20relations
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[8FC5E58BFC30]
n3:nazevZdroje
International Journal of Theoretical Physics
n3:obor
n10:BE
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:rokUplatneniVysledku
n15:2013
n3:svazekPeriodika
52
n3:tvurceVysledku
Skála, Lubomír
n3:wos
000324099800004
s:issn
0020-7748
s:numberOfPages
12
n19:doi
10.1007/s10773-013-1640-1
n13:organizacniJednotka
11320