Record Details

Variational aspects of the Klein-Gordon equation

DSpace at IIT Bombay

View Archive Info
 
 
Field Value
 
Title Variational aspects of the Klein-Gordon equation
 
Creator DATTA, SN
GHOSH, A
CHAKRABORTY, R
 
Subject FUNCTIONAL VARIABLE METHOD
BOUND-STATE SOLUTIONS
N-BOSON SYSTEMS
DIFFERENTIAL-EQUATIONS
MINIMAX TECHNIQUE
ITERATION METHOD
POTENTIAL MODEL
ONE-ELECTRON
VECTOR
SCALAR
Klein-Gordon equation
Min-min theorem
Comparison theorems
 
Description We consider the single-particle, Klein-Gordon equation that is written as first-order in time. The corresponding wave function has two components that are related to each other. For a trial two-component normalizable function that represents a bound state, the optimum upper component-lower component coupling operator is found. It corresponds to an energy minimum. A further variation of the upper component leads to a min-min theorem. Two comparison theorems were suggested by Hall et al. (J Math Phys 45: 3086, 2004), Hall and Lucha (J Phys A 41: 355202, 2008) and Hall and Aliyu (Phys Rev A 78: 052115, 2008) for the second-order Klein-Gordon equation for a particle moving in an attractive central potential. These are verified here from the two-component approach. An additional relation is obtained for an externally applied uniform magnetic field. The derived results are explicitly discussed in the case of Coulomb potential.
 
Publisher INDIAN ASSOC CULTIVATION SCIENCE
 
Date 2016-01-14T12:43:30Z
2016-01-14T12:43:30Z
2015
 
Type Article
 
Identifier INDIAN JOURNAL OF PHYSICS, 89(2)181-187
0973-1458
0974-9845
http://dx.doi.org/10.1007/s12648-014-0506-6
http://dspace.library.iitb.ac.in/jspui/handle/100/17527
 
Language en