TITLE:
New Possibilities of Harmonic Oscillator Basis Application for Quantum System Description. Two Particles with Coulomb Interaction
AUTHORS:
Algirdas Deveikis, Gintautas P. Kamuntavičius
KEYWORDS:
Harmonic Oscillator Basis, Spurious States, Variational Method, Quantum Systems with Coulomb Potential
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.4,
March
19,
2015
ABSTRACT: This
paper is addressed to the problem of Galilei invariant basis construction for identical
fermions systems. The recently introduced method for spurious state elimination
from expansions in harmonic oscillator basis [1]
08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310034003400340037003600360038000000
is adopted and applied to bound states of two particles system with Coulomb
potential description. Traditional expansions in this case demonstrate the extremely
well-known slow convergence, and hence this is the best problem with known
exact solutions for the test of the method. Obtained results demonstrate the
significant simplification of the problem and fast convergence of expansions.
We show that the application of this general method is very efficient in a test
case of the energy spectrum calculation problem of two particles with different
masses interacting with Coulomb potential.