What is the boundary condition for the radial wave function of the Schrödinger equation?
There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin, particularly for singular potentials. A careful derivation of th...
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| Veröffentlicht in: | American journal of physics 2011-06, Vol.79 (6), p.668-671 |
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| container_title | American journal of physics |
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| creator | Khelashvili, Anzor A. Nadareishvili, Teimuraz P. |
| description | There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin, particularly for singular potentials. A careful derivation of the radial Schrödinger equation leads to the appearance of a delta function term when the Laplace operator is written in spherical coordinates. As a result, regardless of the behavior of the potential, an additional constraint is imposed on the radial wave function in the form of a vanishing boundary condition at the origin. |
| doi_str_mv | 10.1119/1.3546099 |
| format | Article |
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Nevertheless, there is no consensus about the behavior of the radial function at the origin, particularly for singular potentials. A careful derivation of the radial Schrödinger equation leads to the appearance of a delta function term when the Laplace operator is written in spherical coordinates. As a result, regardless of the behavior of the potential, an additional constraint is imposed on the radial wave function in the form of a vanishing boundary condition at the origin.</description><identifier>ISSN: 0002-9505</identifier><identifier>EISSN: 1943-2909</identifier><identifier>DOI: 10.1119/1.3546099</identifier><identifier>CODEN: AJPIAS</identifier><language>eng</language><publisher>Woodbury: American Institute of Physics</publisher><subject>Boundary conditions ; Laplace transforms ; Quantum physics ; Schrodinger equation</subject><ispartof>American journal of physics, 2011-06, Vol.79 (6), p.668-671</ispartof><rights>American Association of Physics Teachers</rights><rights>Copyright American Institute of Physics Jun 2011</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c326t-98a65046652494f9d8fc4c3f8372c0042ee1a435d1710a94ee7d2b47ce5e907d3</citedby><cites>FETCH-LOGICAL-c326t-98a65046652494f9d8fc4c3f8372c0042ee1a435d1710a94ee7d2b47ce5e907d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/ajp/article-lookup/doi/10.1119/1.3546099$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,784,794,4512,27924,27925,76256</link.rule.ids></links><search><creatorcontrib>Khelashvili, Anzor A.</creatorcontrib><creatorcontrib>Nadareishvili, Teimuraz P.</creatorcontrib><title>What is the boundary condition for the radial wave function of the Schrödinger equation?</title><title>American journal of physics</title><description>There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin, particularly for singular potentials. A careful derivation of the radial Schrödinger equation leads to the appearance of a delta function term when the Laplace operator is written in spherical coordinates. As a result, regardless of the behavior of the potential, an additional constraint is imposed on the radial wave function in the form of a vanishing boundary condition at the origin.</description><subject>Boundary conditions</subject><subject>Laplace transforms</subject><subject>Quantum physics</subject><subject>Schrodinger equation</subject><issn>0002-9505</issn><issn>1943-2909</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsL3yC4U5ia68xkJVK8QcGFirgKaS42pU6myUzFF_MFfDGn06ILwdXh8H38h_MDcIzRCGMszvGIcpYjIXbAAAtGMyKQ2AUDhBDJBEd8HxykNO9WgUs0AC_PM9VAn2Azs3Aa2sqo-AF1qIxvfKigC7FHURmvFvBdrSx0baV7GFzPHvQsfn0aX73aCO2yVWt4cQj2nFoke7SdQ_B0ffU4vs0m9zd348tJpinJm0yUKueI5TknTDAnTOk009SVtCAaIUasxYpRbnCBkRLM2sKQKSu05VagwtAhONnk1jEsW5saOQ9trLqTsiwIZSLnZSedbiQdQ0rROllH_9a9KjGS6-IkltviOvds4ybtm_6XH3kV4q8oa-P-k_8mfwNNO3w1</recordid><startdate>20110601</startdate><enddate>20110601</enddate><creator>Khelashvili, Anzor A.</creator><creator>Nadareishvili, Teimuraz P.</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20110601</creationdate><title>What is the boundary condition for the radial wave function of the Schrödinger equation?</title><author>Khelashvili, Anzor A. ; Nadareishvili, Teimuraz P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c326t-98a65046652494f9d8fc4c3f8372c0042ee1a435d1710a94ee7d2b47ce5e907d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Boundary conditions</topic><topic>Laplace transforms</topic><topic>Quantum physics</topic><topic>Schrodinger equation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Khelashvili, Anzor A.</creatorcontrib><creatorcontrib>Nadareishvili, Teimuraz P.</creatorcontrib><collection>CrossRef</collection><jtitle>American journal of physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Khelashvili, Anzor A.</au><au>Nadareishvili, Teimuraz P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>What is the boundary condition for the radial wave function of the Schrödinger equation?</atitle><jtitle>American journal of physics</jtitle><date>2011-06-01</date><risdate>2011</risdate><volume>79</volume><issue>6</issue><spage>668</spage><epage>671</epage><pages>668-671</pages><issn>0002-9505</issn><eissn>1943-2909</eissn><coden>AJPIAS</coden><abstract>There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin, particularly for singular potentials. A careful derivation of the radial Schrödinger equation leads to the appearance of a delta function term when the Laplace operator is written in spherical coordinates. As a result, regardless of the behavior of the potential, an additional constraint is imposed on the radial wave function in the form of a vanishing boundary condition at the origin.</abstract><cop>Woodbury</cop><pub>American Institute of Physics</pub><doi>10.1119/1.3546099</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0002-9505 |
| ispartof | American journal of physics, 2011-06, Vol.79 (6), p.668-671 |
| issn | 0002-9505 1943-2909 |
| language | eng |
| recordid | cdi_scitation_primary_10_1119_1_3546099 |
| source | American Institute of Physics (AIP) Journals |
| subjects | Boundary conditions Laplace transforms Quantum physics Schrodinger equation |
| title | What is the boundary condition for the radial wave function of the Schrödinger equation? |
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