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Modified WKB approximation
In the WKB approximation the \nabla^2S term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the \nabla^2 S term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction...
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| Lenguaje: | eng |
| Publicado: |
1995
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| Acceso en línea: | http://cds.cern.ch/record/277933 |
| _version_ | 1780887682832924672 |
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| author | Bronzan, J.B. |
| author_facet | Bronzan, J.B. |
| author_sort | Bronzan, J.B. |
| collection | CERN |
| description | In the WKB approximation the \nabla^2S term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the \nabla^2 S term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to \phi^4 field theory. |
| id | cern-277933 |
| institution | Organización Europea para la Investigación Nuclear |
| language | eng |
| publishDate | 1995 |
| record_format | invenio |
| spelling | cern-2779332023-03-14T18:55:56Zhttp://cds.cern.ch/record/277933engBronzan, J.B.Modified WKB approximationParticle Physics - PhenomenologyIn the WKB approximation the \nabla^2S term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the \nabla^2 S term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to \phi^4 field theory.In the WKB approximation the $\nabla~2S$ term in Schrodinger's equation is subordinate to the |\nabla S|~2 term. Here we study an anti-WKB approximation in which the $\nabla~2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $\phi~4$ field theory.In the WKB approximation the $\nabla~2S$ term in Schrodinger's equation is subordinate to the |\nabla S|~2 term. Here we study an anti-WKB approximation in which the $\nabla~2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $\phi~4$ field theory.In the WKB approximation the $\nabla^2S$ term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the $\nabla^2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $\phi^4$ field theory.hep-ph/9503225CERN-TH-95-56RU-95-11CERN-TH-95-56RU-95-11oai:cds.cern.ch:2779331995-03-03 |
| spellingShingle | Particle Physics - Phenomenology Bronzan, J.B. Modified WKB approximation |
| title | Modified WKB approximation |
| title_full | Modified WKB approximation |
| title_fullStr | Modified WKB approximation |
| title_full_unstemmed | Modified WKB approximation |
| title_short | Modified WKB approximation |
| title_sort | modified wkb approximation |
| topic | Particle Physics - Phenomenology |
| url | http://cds.cern.ch/record/277933 |
| work_keys_str_mv | AT bronzanjb modifiedwkbapproximation |