Matrix Elements of a Fermion System in a Representation of Correlated Basis Functions
Abstract
The ground state and low excited states of liquid He^{3} (and other fermion systems) can be constructed from a set of basis functions Ψ(n)=ψ_{0}^{B}Φ(n) in which ψ_{0}^{B} is the groundstate bosontype solution of the Schrödinger equation and the model functions Φ(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 clusterexpansion technique. An orthonormal basis system is constructed from Ψ(n) and used to express the Hamiltonian operator in quasiparticle form: a large diagonal component containing constant, linear, quadratic, and cubic terms in freequasiparticle occupationnumber operators and a nondiagonal component representing the residual interactions involved in collisions of two and three free quasiparticles.
 Publication:

Physical Review
 Pub Date:
 January 1965
 DOI:
 10.1103/PhysRev.137.A391
 Bibcode:
 1965PhRv..137..391F