Quantum Hydrodynamics: Kirchhoff Equations
In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of n point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demo...
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Veröffentlicht in: | Foundations of physics 2019-04, Vol.49 (4), p.351-364 |
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description | In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of
n
point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial wave approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions. |
doi_str_mv | 10.1007/s10701-019-00252-4 |
format | Article |
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n
point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial wave approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions.</description><identifier>ISSN: 0015-9018</identifier><identifier>EISSN: 1572-9516</identifier><identifier>DOI: 10.1007/s10701-019-00252-4</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Classical and Quantum Gravitation ; Classical Mechanics ; Fluid dynamics ; Fluid flow ; Fluid mechanics ; Hermite polynomials ; History and Philosophical Foundations of Physics ; Hydrodynamics ; Mathematical analysis ; Philosophy of Science ; Physics ; Physics and Astronomy ; Quantum mechanics ; Quantum Physics ; Relativity Theory ; Schrodinger equation ; Statistical Physics and Dynamical Systems ; Vortices</subject><ispartof>Foundations of physics, 2019-04, Vol.49 (4), p.351-364</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-bcd1b8a117b71d608fa0394b7bafa2f2033f125cda09b6edadb85d5c2faa77093</citedby><cites>FETCH-LOGICAL-c319t-bcd1b8a117b71d608fa0394b7bafa2f2033f125cda09b6edadb85d5c2faa77093</cites><orcidid>0000-0002-6447-2010</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10701-019-00252-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10701-019-00252-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Chaitanya, K. V. S. Shiv</creatorcontrib><title>Quantum Hydrodynamics: Kirchhoff Equations</title><title>Foundations of physics</title><addtitle>Found Phys</addtitle><description>In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of
n
point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial wave approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions.</description><subject>Classical and Quantum Gravitation</subject><subject>Classical Mechanics</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Fluid mechanics</subject><subject>Hermite polynomials</subject><subject>History and Philosophical Foundations of Physics</subject><subject>Hydrodynamics</subject><subject>Mathematical analysis</subject><subject>Philosophy of Science</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum mechanics</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Schrodinger equation</subject><subject>Statistical Physics and Dynamical Systems</subject><subject>Vortices</subject><issn>0015-9018</issn><issn>1572-9516</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kMFLwzAUh4MoOKf_gKeBNyH6Xto0jTcZ04kDEfQcXpLGdbjWJe1h_72dFbx5epfv-z34GLtEuEEAdZsQFCAH1BxASMHzIzZBqQTXEotjNgFAyTVgecrOUtoAgFZFPmHXrz01Xb-dLfc-tn7f0LZ26W72XEe3XrchzBa7nrq6bdI5Own0maqL3ztl7w-Lt_mSr14en-b3K-4y1B23zqMtCVFZhb6AMhBkOrfKUiARBGRZQCGdJ9C2qDx5W0ovnQhESoHOpuxq3P2K7a6vUmc2bR-b4aURAqVUIOWBEiPlYptSrIL5ivWW4t4gmEMTMzYxQxPz08Tkg5SNUhrg5qOKf9P_WN_kgWPV</recordid><startdate>20190401</startdate><enddate>20190401</enddate><creator>Chaitanya, K. V. S. Shiv</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-6447-2010</orcidid></search><sort><creationdate>20190401</creationdate><title>Quantum Hydrodynamics: Kirchhoff Equations</title><author>Chaitanya, K. V. S. Shiv</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-bcd1b8a117b71d608fa0394b7bafa2f2033f125cda09b6edadb85d5c2faa77093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Classical Mechanics</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Fluid mechanics</topic><topic>Hermite polynomials</topic><topic>History and Philosophical Foundations of Physics</topic><topic>Hydrodynamics</topic><topic>Mathematical analysis</topic><topic>Philosophy of Science</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum mechanics</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Schrodinger equation</topic><topic>Statistical Physics and Dynamical Systems</topic><topic>Vortices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chaitanya, K. V. S. Shiv</creatorcontrib><collection>CrossRef</collection><jtitle>Foundations of physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chaitanya, K. V. S. Shiv</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantum Hydrodynamics: Kirchhoff Equations</atitle><jtitle>Foundations of physics</jtitle><stitle>Found Phys</stitle><date>2019-04-01</date><risdate>2019</risdate><volume>49</volume><issue>4</issue><spage>351</spage><epage>364</epage><pages>351-364</pages><issn>0015-9018</issn><eissn>1572-9516</eissn><abstract>In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of
n
point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial wave approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10701-019-00252-4</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0002-6447-2010</orcidid></addata></record> |
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subjects | Classical and Quantum Gravitation Classical Mechanics Fluid dynamics Fluid flow Fluid mechanics Hermite polynomials History and Philosophical Foundations of Physics Hydrodynamics Mathematical analysis Philosophy of Science Physics Physics and Astronomy Quantum mechanics Quantum Physics Relativity Theory Schrodinger equation Statistical Physics and Dynamical Systems Vortices |
title | Quantum Hydrodynamics: Kirchhoff Equations |
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