Do Multiquark Hadrons Exist?

The $\mathrm{qq}\overline{\mathrm{qq}}$ system has been examined by solving the four-particle Schrödinger equation variationally. The main findings are that (1) $\mathrm{qq}\overline{\mathrm{qq}}$ bound states normally do not exist, (2) the cryptoexotic $0^{++}$ sector of this system with $K\overline{K}$ quantum numbers is probably the only exception to (1) and its bound states can be identified with the $S^{*}$ and $\delta$ just below $K\overline{K}$ threshold, (3) $\mathrm{qq}\overline{\mathrm{qq}}$ bound states provide a model for the weak binding and color-singlet clustering observed in nuclei, and (4) there is no indication that this system has strong resonances.