Spinless Salpeter equation as a simple matrix eigenvalue problem

We propose a new method for solving the spinless Salpeter equation. Choosing a special set of orthonormal basis functions we are able to calculate analytically the integral over the corresponding kernel as well as the matrix elements of a class of potentials. In this way the problem can be reduced to the solution of a simple matrix eigenvalue problem with explicitly known matrices, which can be solved very fast numerically. The method is demonstrated in detail for $S$ waves using a typical interquark potential as an example.