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Variable operator technique and the min-max theorem

DSpace at IIT Bombay

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Title Variable operator technique and the min-max theorem
 
Creator DATTA, SN
 
Subject dirac-equation
atoms
variable operator
pseudopotential
min-max theorem
relativistic
 
Description We investigate a variation method where the trial function is generated from the application of a variable operator on a reference function. Two conditions are identified, one for obtaining a maximum and another for a minimum. Although the conditions are easy to understand, the overall formulation is somewhat unusual as each condition gives rise to a two-step variation process. As an example, projection operators are used to form the variable operator, and by this tactics one obtains the new interpretation that the pseudopotential formalism is in fact equivalent to a minimax procedure. The two-step variational process is nevertheless more flexible than the pseudopotential formalism, for it can also be used when the variable operator is not manifestly expressed in terms of projectors. This is illustrated by a comparison of the two-step method with the variational solution of Dirac's relativistic electron equation. The same comparison leads to an alternative proof that the process of maximizing energy by varying the u-l coupling operator eliminates ail negative-energy contributions from a trial spinor. The latter observation is crucial for the derivation of the min-max theorem in relativistic quantum mechanics.
 
Publisher INDIAN ACADEMY SCIENCES
 
Date 2011-08-02T09:29:11Z
2011-12-26T12:53:49Z
2011-12-27T05:40:52Z
2011-08-02T09:29:11Z
2011-12-26T12:53:49Z
2011-12-27T05:40:52Z
2000
 
Type Article
 
Identifier PRAMANA-JOURNAL OF PHYSICS, 55(3), 383-392
0304-4289
http://dx.doi.org/10.1007/s12043-000-0068-3
http://dspace.library.iitb.ac.in/xmlui/handle/10054/8745
http://hdl.handle.net/10054/8745
 
Language en