For the quasi one-dimensional electron systems with coulomb interaction, the many-body wave function is obtained on the basis of the correlation oscillation behavior of the electron gas, and the electron correlation function g (|z12|) for quasi one-dimensional systems has been calculated in this paper.
For the quasi one-dimensional electron systems with coulomb interaction, a new model is presented. The form of effective Coulomb potential is derived. Based on the correlated wave function theory, the many-body wave function is obtained on the basis of the collective oscillation behavior of the electron gas. The pair correlation functions and correlation energies of the different electron densities are obtained. The pair correlation functions obtained in this paper are positive definite and satisfy the normalization condition.
We present analytical and numerical results for the pair-correlation function g(r=0) of the electron gas with long-range Coulomb interaction obtained within the ladder theory. Analytical results obtained by perturbation calculation and a Pad\'e approximation are derived and are found to be in good agreement with our numerical solution of the ladder equation. Finite-width effects in the two-dimensional electron gas (quantum well) are also described. For quasi-one-dimensional systems (quantum wires) numerical and analytical results are derived for an oscillator confinement model.