Caustic problems in quantum mechanics with applications to scattering theory
We present a detailed discussion of the semiclassical approximations to path integrals when there exist caustics in the relevant family of classical trajectories. We show carefully how the Airy functions arise from the post-semiclassical approximation of the path integral and interpret the coefficie...
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| Veröffentlicht in: | Phys. Rev. D; (United States) 1983-01, Vol.28 (10), p.2526-2546 |
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| container_end_page | 2546 |
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| container_issue | 10 |
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| container_title | Phys. Rev. D; (United States) |
| container_volume | 28 |
| creator | DEWITT-MORETTE, C NELSON, B TIAN-RONG ZHANG |
| description | We present a detailed discussion of the semiclassical approximations to path integrals when there exist caustics in the relevant family of classical trajectories. We show carefully how the Airy functions arise from the post-semiclassical approximation of the path integral and interpret the coefficients in the Airy functions in terms of the flow of classical trajectories. Finally, we present a configuration-space path integral for the scattering matrix and extend our discussion of caustics to the case of rainbow scattering. |
| doi_str_mv | 10.1103/PhysRevD.28.2526 |
| format | Article |
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We show carefully how the Airy functions arise from the post-semiclassical approximation of the path integral and interpret the coefficients in the Airy functions in terms of the flow of classical trajectories. Finally, we present a configuration-space path integral for the scattering matrix and extend our discussion of caustics to the case of rainbow scattering.</description><identifier>ISSN: 0556-2821</identifier><identifier>EISSN: 1089-4918</identifier><identifier>DOI: 10.1103/PhysRevD.28.2526</identifier><identifier>CODEN: PRVDAQ</identifier><language>eng</language><publisher>Ridge, NY: American Physical Society</publisher><subject>645500 - High Energy Physics- Scattering Theory- (-1987) ; 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics ; AIRY FUNCTIONS ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; Classical and quantum physics: mechanics and fields ; Exact sciences and technology ; FEYNMAN PATH INTEGRAL ; FUNCTIONS ; INTEGRALS ; MATHEMATICAL MANIFOLDS ; MECHANICS ; Physics ; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS ; PROPAGATOR ; QUANTUM MECHANICS ; SCATTERING ; SEMICLASSICAL APPROXIMATION ; WAVE FUNCTIONS ; WKB APPROXIMATION</subject><ispartof>Phys. 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Rev. D; (United States)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>DEWITT-MORETTE, C</au><au>NELSON, B</au><au>TIAN-RONG ZHANG</au><aucorp>Department of Astronomy and Center for Relativity, The University of Texas, Austin, Texas 78712</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Caustic problems in quantum mechanics with applications to scattering theory</atitle><jtitle>Phys. Rev. D; (United States)</jtitle><date>1983-01-01</date><risdate>1983</risdate><volume>28</volume><issue>10</issue><spage>2526</spage><epage>2546</epage><pages>2526-2546</pages><issn>0556-2821</issn><eissn>1089-4918</eissn><coden>PRVDAQ</coden><abstract>We present a detailed discussion of the semiclassical approximations to path integrals when there exist caustics in the relevant family of classical trajectories. We show carefully how the Airy functions arise from the post-semiclassical approximation of the path integral and interpret the coefficients in the Airy functions in terms of the flow of classical trajectories. Finally, we present a configuration-space path integral for the scattering matrix and extend our discussion of caustics to the case of rainbow scattering.</abstract><cop>Ridge, NY</cop><pub>American Physical Society</pub><doi>10.1103/PhysRevD.28.2526</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0556-2821 |
| ispartof | Phys. Rev. D; (United States), 1983-01, Vol.28 (10), p.2526-2546 |
| issn | 0556-2821 1089-4918 |
| language | eng |
| recordid | cdi_crossref_primary_10_1103_PhysRevD_28_2526 |
| source | American Physical Society Journals |
| subjects | 645500 - High Energy Physics- Scattering Theory- (-1987) 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics AIRY FUNCTIONS CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Classical and quantum physics: mechanics and fields Exact sciences and technology FEYNMAN PATH INTEGRAL FUNCTIONS INTEGRALS MATHEMATICAL MANIFOLDS MECHANICS Physics PHYSICS OF ELEMENTARY PARTICLES AND FIELDS PROPAGATOR QUANTUM MECHANICS SCATTERING SEMICLASSICAL APPROXIMATION WAVE FUNCTIONS WKB APPROXIMATION |
| title | Caustic problems in quantum mechanics with applications to scattering theory |
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