Matrix Elements of a Fermion System in a Representation of Correlated Basis Functions
Eugene Feenberg, Chia-Wei Woo
The ground state and low excited states of liquid ${\mathrm{He}}^{3}$ (and other fermion systems) can be constructed from a set of basis functions $\ensuremath{\Psi}(|\mathrm{n})={{\ensuremath{\psi}}_{0}}^{B}\ensuremath{\Phi}(|\mathrm{n})$ in which ${{\ensuremath{\psi}}_{0}}^{B}$ is the ground-state boson-type solution of the Schr\"odinger equation and the model functions $\ensuremath{\Phi}(|\mathrm{n})$ are Slater determinants suitable for describing states of the noninteracting Fermion system. Diagonal and nondiagonal matrix elements of the identity and the Hamiltonian operator are evaluated by a cluster-expansion technique. An orthonormal basis system is constructed from $\ensuremath{\Psi}(|\mathrm{n})$ and used to express the Hamiltonian operator in quasiparticle form: a large diagonal component containing constant, linear, quadratic, and cubic terms in free-quasiparticle occupation-number operators and a nondiagonal component representing the residual interactions involved in collisions of two and three free quasiparticles.
Physical Review•Jan 18, 1965•45 citations