Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field
Autor(a) principal: | |
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Data de Publicação: | 1990 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevA.42.3744 http://hdl.handle.net/11449/230974 |
Resumo: | The probability amplitude for a spin-1/2 particle in a precessing magnetic field to be in an energy eigenstate is calculated exactly. The probability for the particle to be in a given energy eigenstate and the corresponding phase of the amplitude are obtained. In the adiabatic limit there are no transitions, and the phase is the sum of the dynamical phase and the Berry phase. When a unitary transformation is made, the Hamiltonian and the energy operator transform differently. The energy eigenvalues, Berry phases, and probability amplitudes calculated in a frame rotating with the magnetic field are the same as in the laboratory frame. If the energy operator is incorrectly taken to be the Hamiltonian in the rotating frame, incorrect energy eigenvalues, Berry phases, and probability amplitudes are obtained. Nevertheless, in the adiabatic limit the correct total phase results. © 1990 The American Physical Society. |
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Repositório Institucional da UNESP |
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Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic fieldThe probability amplitude for a spin-1/2 particle in a precessing magnetic field to be in an energy eigenstate is calculated exactly. The probability for the particle to be in a given energy eigenstate and the corresponding phase of the amplitude are obtained. In the adiabatic limit there are no transitions, and the phase is the sum of the dynamical phase and the Berry phase. When a unitary transformation is made, the Hamiltonian and the energy operator transform differently. The energy eigenvalues, Berry phases, and probability amplitudes calculated in a frame rotating with the magnetic field are the same as in the laboratory frame. If the energy operator is incorrectly taken to be the Hamiltonian in the rotating frame, incorrect energy eigenvalues, Berry phases, and probability amplitudes are obtained. Nevertheless, in the adiabatic limit the correct total phase results. © 1990 The American Physical Society.Instituto de Física Teórica, Rua Pamplona 145, 01405 Sao Paulo, Sao PauloInstituto de Física TeóricaKobe, Donald H.Aguilera-Navarro, Valdir C.Kurcbart, Samuel M.Zimerman, Abraham H.2022-04-29T08:42:56Z2022-04-29T08:42:56Z1990-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article3744-3750http://dx.doi.org/10.1103/PhysRevA.42.3744Physical Review A, v. 42, n. 7, p. 3744-3750, 1990.1050-2947http://hdl.handle.net/11449/23097410.1103/PhysRevA.42.37442-s2.0-1542651289Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Ainfo:eu-repo/semantics/openAccess2022-04-29T08:42:56Zoai:repositorio.unesp.br:11449/230974Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:24:59.312408Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field |
title |
Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field |
spellingShingle |
Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field Kobe, Donald H. |
title_short |
Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field |
title_full |
Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field |
title_fullStr |
Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field |
title_full_unstemmed |
Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field |
title_sort |
Exact phases and probabilities for a spin-1/2 particle in a precessing magnetic field |
author |
Kobe, Donald H. |
author_facet |
Kobe, Donald H. Aguilera-Navarro, Valdir C. Kurcbart, Samuel M. Zimerman, Abraham H. |
author_role |
author |
author2 |
Aguilera-Navarro, Valdir C. Kurcbart, Samuel M. Zimerman, Abraham H. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Instituto de Física Teórica |
dc.contributor.author.fl_str_mv |
Kobe, Donald H. Aguilera-Navarro, Valdir C. Kurcbart, Samuel M. Zimerman, Abraham H. |
description |
The probability amplitude for a spin-1/2 particle in a precessing magnetic field to be in an energy eigenstate is calculated exactly. The probability for the particle to be in a given energy eigenstate and the corresponding phase of the amplitude are obtained. In the adiabatic limit there are no transitions, and the phase is the sum of the dynamical phase and the Berry phase. When a unitary transformation is made, the Hamiltonian and the energy operator transform differently. The energy eigenvalues, Berry phases, and probability amplitudes calculated in a frame rotating with the magnetic field are the same as in the laboratory frame. If the energy operator is incorrectly taken to be the Hamiltonian in the rotating frame, incorrect energy eigenvalues, Berry phases, and probability amplitudes are obtained. Nevertheless, in the adiabatic limit the correct total phase results. © 1990 The American Physical Society. |
publishDate |
1990 |
dc.date.none.fl_str_mv |
1990-01-01 2022-04-29T08:42:56Z 2022-04-29T08:42:56Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1103/PhysRevA.42.3744 Physical Review A, v. 42, n. 7, p. 3744-3750, 1990. 1050-2947 http://hdl.handle.net/11449/230974 10.1103/PhysRevA.42.3744 2-s2.0-1542651289 |
url |
http://dx.doi.org/10.1103/PhysRevA.42.3744 http://hdl.handle.net/11449/230974 |
identifier_str_mv |
Physical Review A, v. 42, n. 7, p. 3744-3750, 1990. 1050-2947 10.1103/PhysRevA.42.3744 2-s2.0-1542651289 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review A |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
3744-3750 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129064990408704 |