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Title:  Exact solution of the relativistic dynamics of a spin(1)/(2) particle moving in a homogeneous magnetic field 
Authors:  DATTA, SN MISRA, A 
Issue Date:  2001 
Publisher:  JOHN WILEY & SONS INC 
Citation:  INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 82(5), 209217 
Abstract:  The relativistic dynamics of one spin1/2 particle moving in a uniform magnetic field is described by the Hamiltonian h(D)(0)(pi) = c alpha . pi + beta mc(2). The discrete (and semidiscrete) eigenvalues and the corresponding eigenspinors are in principle known from the work of Dirac, Rabi, and Bloch. These are extensively reviewed here. Next, exact solutions are worked out for the recoil dynamics in relative coordinates, which involves the Hamiltonian h(D)(0)(k) = c alpha . k + beta mc(2). Exact solutions are also explicitly calculated in the case where the spin1/2 particle has an anomalous magnetic moment such that its Hamiltonian is given by h(D)(pi) = h(D)(0)(pi)  beta mu (ano)sigma . B. Similar exact solutions are derived here when the recoiling particle has an anomalous magnetic moment, that is, the eigenvalues and eigenspinors of the Hamiltonian h(D)(k) = h(D)(0)(k)  beta mu (ano)sigma . B are explicitly obtained. The diagonalized and separable form of the Hamiltonian hD(rr), written as (h) over tilde (D)(pi), has exceedingly simple forms of eigenspinors. Similarly, the diagonalized and separable form of the operator h(D)(k), written as (h) over tilde (D)(k), has very simple eigenspinors. The importance of these exact solutions is that the eigenspinors can be used as bases in a calculation involving many spin1/2 particles placed in a uniform magnetic field. (C) 2001 , Inc. 
URI:  http://dx.doi.org/10.1002/qua.1035 http://dspace.library.iitb.ac.in/xmlui/handle/10054/9399 http://hdl.handle.net/10054/9399 
ISSN:  00207608 
Appears in Collections:  Article

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