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Master's Dissertation
DOI
10.11606/D.43.2002.tde-10062003-015716
Document
Author
Full name
Mário César Baldiotti
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2002
Supervisor
Committee
Guitman, Dmitri Maximovitch (President)
Escobar, Bruto Max Pimentel
Frenkel, Josif
Title in Portuguese
"Estados quânticos de um elétron em um campo magnético uniforme"
Keywords in Portuguese
Campo Magnético e Longitudinal
Equação de Dirac e Klein-Gordon
Estados Coerentes
Soluções Exatas
Teoria Quântica Relativística
Abstract in Portuguese
Neste trabalho, apresentamos um método que permite explicitar a arbitrariedade contida nas soluções das equações de onda relativísticas, na presença de certos tipos de campos eletromagnéticos externos. Esta arbitrariedade está relacionada com a existência de uma transformação, com a qual podemos reduzir o número de variáveis presentes na equação original. Através desta transformação, criamos uma representação, a qual permite obter novos conjuntos de soluções exatas e construir a função de evolução para a equação de Klein-Gordon. Como resultado, apresentamos novos conjuntos de soluções, estacionárias e não-estacionárias, para o problema em um campo magnético constante e uniforme e a combinação deste campo com um campo elétrico longitudinal.
Title in English
Quantum States of an Eletcron in a Uniform Magnetic Field
Keywords in English
Coherent states
Dirac and Klein-Gordon Equation
Exact Solutions
Magnetic and Longitudinal field
Relativistic quantum theory
Abstract in English
We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest, and to construct the evolution function to the Klein-Gordon equation. As resulted, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.
 
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dissert.pdf (699.47 Kbytes)
Publishing Date
2003-07-03
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • BAGROV, V. G., et al. New solutions of relativistic wave equations in magnetic fields and longitudinal fields [doi:10.1063/1.1461428]. Journal of Mathematical Physics [online], 2002, vol. 43, n. 5, p. 2284-2305.
  • BAGROV, V. G., BALDIOTTI, M. C., and GITMAN, D. M. Charged particles in crossed and longitudinal electromagnetic fields and beam guides [doi:10.1063/1.2771543]. Journal of Mathematical Physics [online], 2007, vol. 48, n. 8, p. 1-15.
All rights of the thesis/dissertation are from the authors
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