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Series on advances in quantum many-body theory

THEORY OF CORRELATED BASIS FUNCTIONS

E. Krotscheck

Published Aug 1, 2002• 9 citations
Publisher
DOI
10.1142/9789812777072_0007

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A variational wave function constructed with correlated hyperspherical harmonic functions is used to describe the Helium trimer. This system is known to have a deep bound state. In addition, different potential models predict the existence of a shallow excited state that has been identified as an Efimov state. Using the Rayleigh-Ritz variational principle, the energies and wave functions of both bound states have been obtained by solving a generalized eigenvalue problem. The introduction of a suitable correlation factor reduces considerably the dimension of the basis needed to accurately describe the structure of the system. The most recent helium-helium interactions have been investigated.
We developed a many-body method to calculate the electron correlated basis function of excited state. Based on the Chakravarty-Woo equation and functional expansion and convolution approximation, we got the linear integral iteration equation for the variation of density and correlation function, so the wave function, due to electron excitation. A general formula for excitation energy in many-body problem is obtained From this and the known experimental data, we found the energy gap and electron correlation in 1-d conducting polymer. The result is in good accordance with the experiment.