Eur. Phys. J. B 43, 393-398 (2005)
https://doi.org/10.1140/epjb/e2005-00069-7

Rayleigh-Schrödinger-Goldstone variational perturbation theory for many Fermion systems

¹ Institute of Physics and Applied Physics, Yonsei University, Seoul 120-749, Korea
² Department of Physics, University of Incheon, Incheon 402-749, Korea

Corresponding author: ^a skyou@phya.yonsei.ac.kr

Received: 30 June 2004
Published online: 15 March 2005

Abstract

We present a Rayleigh-Schrödinger-Goldstone perturbation formalism for many Fermion systems. Based on this formalism, variational perturbation scheme which goes beyond the Gaussian approximation is developed. In order to go beyond the Gaussian approximation, we identify a parent Hamiltonian which has an effective Gaussian vacuum as a variational solution and carry out further perturbation with respect to the renormalized interaction using Goldstone's expansion. Perturbation rules for the ground state wavefunctional and energy are found, thus, opening a way for general use of the Schrödinger picture method for many Fermion systems. Useful commuting relations between operators and the Gaussian wavefunctional are also found, which could reduce the calculational efforts substantially. As examples, we calculate the first order correction to the Gaussian wavefunctional and the second order correction to the ground state of an electron gas system with the Yukawa-type interaction.