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Virginia Polytechnic Institute and State University
The semiclassical limit of quantum dynamics
Abstract
dc:description.abstractWe study the ħ→0 limit of the quantum dynamics determined by the Hamiltonian H(ħ) = -(ħ²/2m)Δ + Ｖ on L²(ℝ<sup>n</sup>) for a large class of potentials. By convolving with certain Gaussian states we obtain classically determined asymptotic behavior of the quantum evolution of states of compact support. For suitable potentials we obtain the analogus result for the scattering operator in the position representation. For initial or incoming states of class C<sub>o</sub>¹ the error terms are shown to have L² norms of order ħ<sup>½-ε</sup> for arbitrarily small positive ε.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Polytechnic Institute and State University
- Year dc:date.issued
- 1986
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Robinson, Sam Leslie
- Chairs dc:contributor.committeechair
-
- Hagedorn, George
- Ball, Joseph A.
- Kohler, Werner
- Slawny, Joseph
- Zweifel, Paul F.
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en_US
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- http://hdl.handle.net/10919/76489
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/76489