  A method to calculate the bound states of three-atoms without resorting to an
explicit partial wave decomposition is presented. The differential form of the
Faddeev equations in the total angular momentum representation is used for this
purpose. The method utilizes Cartesian coordinates combined with the
tensor-trick preconditioning for large linear systems and Arnoldi's algorithm
for eigenanalysis. As an example, we consider the He$_3$ system in which the
interatomic force has a very strong repulsive core that makes the three-body
calculations with standard methods tedious and cumbersome requiring the
inclusion of a large number of partial waves. The results obtained compare
favorably with other results in the field.
