  This paper reports a detailed description of the equivalent linear two-body
method for the many body problem, which is based on an approximate reduction of
the many-body Schroedinger equation by the use of a variational principle. To
test the accuracy of the method it has been applied to the one-dimensional
N-body problem with pair-wise contact interactions (McGurie-Yang N-body
problem) and to the dilute Bose-Einstein condensation (BEC) of atoms in
harmonic traps at zero temperature. For both cases, it is shown that the method
gives excellent results for large N.
