Quantization as Selection Problem.
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| Title: | Quantization as Selection Problem. |
|---|---|
| Authors: | Enders, Peter1 enders@dekasges.de, Suisky, Dieter2 dsuisky@physik.hu-berlin.de |
| Source: | International Journal of Theoretical Physics. Feb2005, Vol. 44 Issue 2, p161-194. 34p. |
| Subjects: | Geometric quantization, Selection theorems, Differential geometry, Quantum theory, Partial differential equations, Combinatorial set theory, Eigenvalues, Matrices (Mathematics) |
| Abstract: | Quantum systems exhibit a smaller number of energetic states than classical systems (A. Einstein, 1907, Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme, Ann. Phys. 22, 180ff). We take up the selection criterion for this in two parts. (1) The selection problem between classical and nonclassical mechanical systems is formulated in terms of possible and impossible configurations (among others, this overcomes the difficulties occurring when discussing the behavior of quantum particles in terms of paths). (2) The (nonclassical) selection of the quantum states is formulated, using recurrence relations and the energy law. The reformulation of “quantization as eigenvalue problem” in terms of “quantization as selection problem” allows one to derive Schrödinger’s stationary equation from classical mechanics through a straightforward and unique procedure; the nonstationary and multibody equations are subsequently acquired within the same frame. In contrast to the (classical) eigenvalue problem, the (nonclassical) selection problem can be formulated and solved without any reference to additional a priori assumptions on the nature of the quantum system, such as the wave-corpuscle dualism or an underlying wave equation or the existence of Planck’s finite action parameter. The existence of such an additional parameter—as the only additional one—is inherent in the procedure. Within our axiomatic-deductive approach, we modify classical mechanics only where it itself indicates an inherent limitation. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Theoretical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Quantization as Selection Problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Enders%2C+Peter%22">Enders, Peter</searchLink><relatesTo>1</relatesTo><i> enders@dekasges.de</i><br /><searchLink fieldCode="AR" term="%22Suisky%2C+Dieter%22">Suisky, Dieter</searchLink><relatesTo>2</relatesTo><i> dsuisky@physik.hu-berlin.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Theoretical+Physics%22">International Journal of Theoretical Physics</searchLink>. Feb2005, Vol. 44 Issue 2, p161-194. 34p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Geometric+quantization%22">Geometric quantization</searchLink><br /><searchLink fieldCode="DE" term="%22Selection+theorems%22">Selection theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+geometry%22">Differential geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+theory%22">Quantum theory</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+set+theory%22">Combinatorial set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Quantum systems exhibit a smaller number of energetic states than classical systems (A. Einstein, 1907, Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme, Ann. Phys. 22, 180ff). We take up the selection criterion for this in two parts. (1) The selection problem between classical and nonclassical mechanical systems is formulated in terms of possible and impossible configurations (among others, this overcomes the difficulties occurring when discussing the behavior of quantum particles in terms of paths). (2) The (nonclassical) selection of the quantum states is formulated, using recurrence relations and the energy law. The reformulation of “quantization as eigenvalue problem” in terms of “quantization as selection problem” allows one to derive Schrödinger’s stationary equation from classical mechanics through a straightforward and unique procedure; the nonstationary and multibody equations are subsequently acquired within the same frame. In contrast to the (classical) eigenvalue problem, the (nonclassical) selection problem can be formulated and solved without any reference to additional a priori assumptions on the nature of the quantum system, such as the wave-corpuscle dualism or an underlying wave equation or the existence of Planck’s finite action parameter. The existence of such an additional parameter—as the only additional one—is inherent in the procedure. Within our axiomatic-deductive approach, we modify classical mechanics only where it itself indicates an inherent limitation. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Theoretical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10773-005-1491-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 34 StartPage: 161 Subjects: – SubjectFull: Geometric quantization Type: general – SubjectFull: Selection theorems Type: general – SubjectFull: Differential geometry Type: general – SubjectFull: Quantum theory Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Combinatorial set theory Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Matrices (Mathematics) Type: general Titles: – TitleFull: Quantization as Selection Problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Enders, Peter – PersonEntity: Name: NameFull: Suisky, Dieter IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2005 Type: published Y: 2005 Identifiers: – Type: issn-print Value: 00207748 Numbering: – Type: volume Value: 44 – Type: issue Value: 2 Titles: – TitleFull: International Journal of Theoretical Physics Type: main |
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