  The Lagrange mesh method is a very simple procedure to accurately solve
eigenvalue problems starting from a given nonrelativistic or semirelativistic
two-body Hamiltonian with local or nonlocal potential. We show in this work
that it can be applied to solve the inverse problem, namely, to find the
equivalent local potential starting from a particular bound state wave function
and the corresponding energy. In order to check the method, we apply it to
several cases which are analytically solvable: the nonrelativistic harmonic
oscillator and Coulomb potential, the nonlocal Yamaguchi potential and the
semirelativistic harmonic oscillator. The potential is accurately computed in
each case. In particular, our procedure deals efficiently with both
nonrelativistic and semirelativistic kinematics.
