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A Variational Procedure for Hard Core Potential
Abstract
A set of variational calculations has been carried out with suitable trial wave functions constructed to conform with the features and boundary conditions imposed by the hard core. The form of the trial function is suggested by perturbation theory and it is rather straightforward so that it can be used in complicated problems, The method has been justified for the cases without hard core such as Mathieu's Equation and the harmonic oscillator, and the eigenvalues in the former case are improved by this method over results obtained by refined perturbation procedures. The harmonic oscillators with an infinitely repulsive region of various radii have been considered to test the procedure and to see the variation of energy with the core radius. The problem was solved approximately by two other methods, numerical Integration and perturbation theory. We find that these three results agree to at least two signifi cant digits in the eigenvalues for the largest size of core and note especially that the latter two agree to in the first three digits. Finally the procedure is applied to the deuteron with the Brueckner-Oammel potential, resulting in a fairly good approximation in both binding energy and the wave function. In this case again the second order variational calculations yield binding energy with an accuracy of at least two significant digits.
Subject Area
Nuclear physics
Recommended Citation
KOH, YOON SUK, "A Variational Procedure for Hard Core Potential" (1963). ETD collection for University of Nebraska-Lincoln. AAI6304778.
https://digitalcommons.unl.edu/dissertations/AAI6304778