Academic Journal
On some states minimizing uncertainty relations: A new look at these relations.
| Title: | On some states minimizing uncertainty relations: A new look at these relations. |
|---|---|
| Authors: | Urbanowski, K.1 (AUTHOR) K.Urbanowski@if.uz.zgora.pl |
| Source: | Modern Physics Letters A. 7/10/2026, Vol. 41 Issue 21, p1-12. 12p. |
| Subject Terms: | *Standard deviations, *Heisenberg uncertainty principle, *Uncertainty (Information theory), *Quantum states, *Statistical correlation |
| Abstract: | The Heisenberg–Robertson (HR) and Robertson–Schrödinger (RS) uncertainty relations are studied. Analyzing the RS uncertainty relation we found, that there can exist a large set of states of the quantum system under considerations, for which the lower bound of the product of the standard deviations of a pair of noncommuting observables, A and B, is zero, and which differ from those described in the literature for the HR uncertainty relation. These states are not eigenstates of either the observable A or B. The correlation function for these observables in such states is equal to zero. We have also shown that the so-called "sum uncertainty relations" also do not provide any information about lower bounds on the standard deviations calculated for these states. We additionally show that the uncertainty principle in its most general form has two faces: One is that it is a lower bound on the product of standard deviations, and the other is that the product of standard deviations is an upper bound on the modulus of the correlation function of a pair of the noncommuting observables in the state under consideration. [ABSTRACT FROM AUTHOR] |
| Database: | Academic Search Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: asx DbLabel: Academic Search Index An: 194725839 RelevancyScore: 1452 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1452.42199707031 |
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| Items | – Name: Title Label: Title Group: Ti Data: On some states minimizing uncertainty relations: A new look at these relations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Urbanowski%2C+K%2E%22">Urbanowski, K.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> K.Urbanowski@if.uz.zgora.pl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Modern+Physics+Letters+A%22">Modern Physics Letters A</searchLink>. 7/10/2026, Vol. 41 Issue 21, p1-12. 12p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Standard+deviations%22">Standard deviations</searchLink><br />*<searchLink fieldCode="DE" term="%22Heisenberg+uncertainty+principle%22">Heisenberg uncertainty principle</searchLink><br />*<searchLink fieldCode="DE" term="%22Uncertainty+%28Information+theory%29%22">Uncertainty (Information theory)</searchLink><br />*<searchLink fieldCode="DE" term="%22Quantum+states%22">Quantum states</searchLink><br />*<searchLink fieldCode="DE" term="%22Statistical+correlation%22">Statistical correlation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The Heisenberg–Robertson (HR) and Robertson–Schrödinger (RS) uncertainty relations are studied. Analyzing the RS uncertainty relation we found, that there can exist a large set of states of the quantum system under considerations, for which the lower bound of the product of the standard deviations of a pair of noncommuting observables, A and B, is zero, and which differ from those described in the literature for the HR uncertainty relation. These states are not eigenstates of either the observable A or B. The correlation function for these observables in such states is equal to zero. We have also shown that the so-called "sum uncertainty relations" also do not provide any information about lower bounds on the standard deviations calculated for these states. We additionally show that the uncertainty principle in its most general form has two faces: One is that it is a lower bound on the product of standard deviations, and the other is that the product of standard deviations is an upper bound on the modulus of the correlation function of a pair of the noncommuting observables in the state under consideration. [ABSTRACT FROM AUTHOR] |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=194725839 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0217732326501063 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 1 Subjects: – SubjectFull: Standard deviations Type: general – SubjectFull: Heisenberg uncertainty principle Type: general – SubjectFull: Uncertainty (Information theory) Type: general – SubjectFull: Quantum states Type: general – SubjectFull: Statistical correlation Type: general Titles: – TitleFull: On some states minimizing uncertainty relations: A new look at these relations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Urbanowski, K. IsPartOfRelationships: – BibEntity: Dates: – D: 10 M: 07 Text: 7/10/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02177323 Numbering: – Type: volume Value: 41 – Type: issue Value: 21 Titles: – TitleFull: Modern Physics Letters A Type: main |
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