Equivalent linear two-body method for many-body problems

We present a detailed description of the equivalent linear two-body method for the many-body problem, which is based on an approximate reduction of th e many-body Schrodinger equation by the use of a variational principle. The method has been applied to the one-dimensional N-body problem with pair-wi se contact interactions (McGurie-Yang N-body problem) and to the dilute Bos e-Einstein condensation of atoms in harmonic traps at zero temperature for both positive and negative scattering lengths. The ground state energy and wavefunction for a dilute Bose gas are obtained analytically for large valu e of N and it is shown that the method gives excellent results in the large -N limit.