When can identical particles collide ?
It is customary, when discussing configuration spaces of identical particles in two or more dimensions, to discard the configurations where two or more particles overlap, the justification being that the configuration space ceases to be a manifold at those points, and also to allow for nonbosonic st...
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| Veröffentlicht in: | Physical review. D, Particles and fields Particles and fields, 1992-01, Vol.45 (2), p.687-696 |
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| container_end_page | 696 |
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| container_title | Physical review. D, Particles and fields |
| container_volume | 45 |
| creator | BOURDEAU, M SORKIN, R. D |
| description | It is customary, when discussing configuration spaces of identical particles in two or more dimensions, to discard the configurations where two or more particles overlap, the justification being that the configuration space ceases to be a manifold at those points, and also to allow for nonbosonic statistics. We show that there is in general a loss of physical information in discarding these points by studying the simple system of two free particles moving in the plane and requiring that the Hamiltonian be self-adjoint. We find that the Hamiltonian for fermions is unique, but that in all other cases (i.e., for particles obeying properly fractional or Bose statistics) there is a one-parameter family of possible self-adjoint extensions. We show how a plausible limiting procedure selects a unique extension from each family, the favored extension being the one for which the wave function remains finite at the points of overlap. We also test our procedure by applying it to the known case of the hydrogen atom. |
| doi_str_mv | 10.1103/PhysRevD.45.687 |
| format | Article |
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D, Particles and fields</jtitle><addtitle>Phys Rev D Part Fields</addtitle><date>1992-01-15</date><risdate>1992</risdate><volume>45</volume><issue>2</issue><spage>687</spage><epage>696</epage><pages>687-696</pages><issn>0556-2821</issn><eissn>1089-4918</eissn><coden>PRVDAQ</coden><abstract>It is customary, when discussing configuration spaces of identical particles in two or more dimensions, to discard the configurations where two or more particles overlap, the justification being that the configuration space ceases to be a manifold at those points, and also to allow for nonbosonic statistics. We show that there is in general a loss of physical information in discarding these points by studying the simple system of two free particles moving in the plane and requiring that the Hamiltonian be self-adjoint. We find that the Hamiltonian for fermions is unique, but that in all other cases (i.e., for particles obeying properly fractional or Bose statistics) there is a one-parameter family of possible self-adjoint extensions. We show how a plausible limiting procedure selects a unique extension from each family, the favored extension being the one for which the wave function remains finite at the points of overlap. We also test our procedure by applying it to the known case of the hydrogen atom.</abstract><cop>Ridge, NY</cop><pub>American Physical Society</pub><pmid>10014422</pmid><doi>10.1103/PhysRevD.45.687</doi><tpages>10</tpages></addata></record> |
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| identifier | ISSN: 0556-2821 |
| ispartof | Physical review. D, Particles and fields, 1992-01, Vol.45 (2), p.687-696 |
| issn | 0556-2821 1089-4918 |
| language | eng |
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| source | American Physical Society Journals |
| subjects | 661100 - Classical & Quantum Mechanics- (1992-) ATOMS BOSE-EINSTEIN STATISTICS BOUNDARY CONDITIONS CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Classical and quantum physics: mechanics and fields ELEMENTS Exact sciences and technology FERMIONS FUNCTIONS HAMILTONIANS HYDROGEN INTERACTIONS MANY-BODY PROBLEM MATHEMATICAL OPERATORS NONMETALS PARTICLE INTERACTIONS Physics QUANTUM OPERATORS Theory of quantized fields THREE-DIMENSIONAL CALCULATIONS TWO-BODY PROBLEM WAVE FUNCTIONS |
| title | When can identical particles collide ? |
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