Matrix elements of a many-boson Hamiltonian in a representation of correlated basis functions

Abstract

The set of basis functions $$\Psi = \psi \prod\limits_i {\rho _{k_i } } $$ in which Ψ is a real correlation factor and ρk is the Fourier component of the density operator, is useful in describing the ground and low excited states of a many-boson system such as liquid4He. We consider the problem of computing the matrix elements of the Hamiltonian in this representation. A closed expression is obtained for the general matrix element, and examples which involve the phonon splitting and coalescing states are given.