Four-body bound states from the Schrödinger equation with separable potentials

The coupled, two-variable integral equations that determine the four-body bound state, when the interactions are represented by separable potentials, are derived from the Schrödinger equation instead of the Yakubovsky $t$-matrix equations. The integral equations are solved numerically for simple $s$-wave potentials without resort to separable expansions of their kernels. For rank-one potentials the $\alpha$ particle is severely overbound. Sensitivity to the singlet effective range and the tensor component of the triplet interaction is discussed.