The Lagrange mesh method is a very powerful procedure to compute eigenvalues and eigenfunctions of nonrelativistic Hamiltonians. The trial eigenstates are developed in a basis of well-chosen functions and the computation of Hamiltonian matrix elements requires only the evaluation of the potential at grid points. It is shown that this method can be used to solve semirelativistic two-body eigenvalue equations. As in the nonrelativistic case, it is very accurate, fast, and very simple to implement.

• Received 19 February 2001

DOI:https://doi.org/10.1103/PhysRevE.64.016703