Continued fractions and the harmonic oscillator using Feynman’s path integrals

Title:
Continued fractions and the harmonic oscillator using Feynman’s path integrals
Authors:
Winters, Ron; English, Lars
Citation:
"Continued fractions and the harmonic oscillator using Feynman's path integrals," by L. Q. English and R. R. Winters [Am. J. Phys. 65 (5), 390–393 (1997).
Publisher:
American Journal of Physics
DATE ISSUED:
May-1997
PERMANENT LINK:
http://hdl.handle.net/2374.DEN/5022; http://hdl.handle.net/2374
Type:
Article
Language:
en_US
Description:
The Simple Harmonic Oscillator plays a prominent role in most undergraduate Quantum Mechanics courses. The study of this system using path integrals can serve to introduce a formulation of Quantum Mechanics which is usually considered beyond the scope of most undergraduate courses. However given the current interest in the interpretation and foundations of Quantum Mechanics, non-standard approaches such as Feynman’s path integral formalism can be helpful in developing insights into the structure of Quantum Mechanics. In this paper we evaluate the path integration appearing in Feynman’s treatment in a natural and direct manner utilizing a symbolic computational program. This approach makes the use of the path integral formulation of Quantum Mechanics accessible to most undergraduate physics majors. As a byproduct of our approach, we find a representation of the reciprocal of the sinc function, . . ., in terms of an infinite product of partial approximates of a continued fraction. We have not found this representation in the literature.
ISSN:
00029595; 00029505
Appears in Collections:
Faculty Publications

Full metadata record

DC FieldValue Language
dc.contributor.authorWinters, Ronen
dc.contributor.authorEnglish, Larsen
dc.date.accessioned2013-01-02T18:07:20Zen
dc.date.accessioned2013-12-18T21:06:12Z-
dc.date.available2013-01-02T18:07:20Zen
dc.date.available2013-12-18T21:06:12Z-
dc.date.created1997-05en
dc.date.issued1997-05en
dc.identifier.citation"Continued fractions and the harmonic oscillator using Feynman's path integrals," by L. Q. English and R. R. Winters [Am. J. Phys. 65 (5), 390–393 (1997).en_US
dc.identifier.issn00029595en
dc.identifier.issn00029505en
dc.identifier.urihttp://hdl.handle.net/2374.DEN/5022en
dc.identifier.urihttp://hdl.handle.net/2374-
dc.descriptionThe Simple Harmonic Oscillator plays a prominent role in most undergraduate Quantum Mechanics courses. The study of this system using path integrals can serve to introduce a formulation of Quantum Mechanics which is usually considered beyond the scope of most undergraduate courses. However given the current interest in the interpretation and foundations of Quantum Mechanics, non-standard approaches such as Feynman’s path integral formalism can be helpful in developing insights into the structure of Quantum Mechanics. In this paper we evaluate the path integration appearing in Feynman’s treatment in a natural and direct manner utilizing a symbolic computational program. This approach makes the use of the path integral formulation of Quantum Mechanics accessible to most undergraduate physics majors. As a byproduct of our approach, we find a representation of the reciprocal of the sinc function, . . ., in terms of an infinite product of partial approximates of a continued fraction. We have not found this representation in the literature.en_US
dc.language.isoen_USen_US
dc.publisherAmerican Journal of Physicsen_US
dc.relation.ispartofFaculty Publicationsen_US
dc.titleContinued fractions and the harmonic oscillator using Feynman’s path integralsen_US
dc.typeArticleen_US
dc.contributor.institutionDenison Universityen_US
dc.date.digitized2013-01-02en
dc.contributor.repositoryDenison Resource Commonsen_US
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