Premium
Density and Correlations in Large One and Three Dimensional Systems of Fermions
Author(s) -
Ullah N.
Publication year - 1989
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190371103
Subject(s) - fermion , physics , harmonic oscillator , hamiltonian (control theory) , quantum mechanics , isobar , density of states , eigenvalues and eigenvectors , coulomb , nucleon , mathematical physics , quantum electrodynamics , mathematics , particle physics , mathematical optimization , electron
The density and correlations are studied for a system of fermions moving in an average harmonic oscillator potential in one and three dimensions when the number of fermions are large. The technique is based on the use of Mehler's formula for the product of two Hermite functions and con‐. tour integrations. Wigner transform is then calculated using this technique. It is shown that it becomes a step function when number of fermions become large. By integrating out momenta, an expression for the density of fermions is derived. Two‐particle correlation function is studied in detail. Dyson's type of correlations for a system of nucleons is studied. The connection between one dimensional system of fermions and eigenvalues of a random Hermitean Hamiltonian is shown. The Coulomb energy difference of isobars is studied using nucleon density and correlations.