Few-body anharmonic oscillators and the matrix continued fractions

For both identical and distinguishable particles and for an arbitrary polynomial approximation to the realistic two-body forces, the A-body Hamiltonian may be converted into an infinite block-three-diagonal matrix in the properly arranged, translationally invariant, oscillator basis. As a consequence, the exact Green function and all the projections of eigenstates of the microscopic Schrodinger equation become expressible in terms of the matrix continued fractions. This generalises the recent reformulation of the one-dimensional A=1 anharmonic problem by Graffi and Greechi (1975). The quick convergence of this non-perturbative method of solving the many-body bound-state problem is demonstrated for the simplest three- and four-body examples. With the core-possessing type V(r)=-r²+r⁴ of the spin- and isospin-independent two-body interaction, only the 10^-3 error in the three-bosonic ground-state energy arises from restricting the formulae to 5*5 dimensional matrices.