Abstract
A new method for the determination of the eigenvalues of any diatomic potential U(r) is presented. An eigenvalue function F(E) is associated to U(r), where E is a variable. It is shown that the eigenvalues of U are the zeros of the function F. A numerical application to the Morse potential of the B-H2+ state is presented. The error of the new method is compared with those of the methods is compared with those of the methods of Hajj (1980) and Cooley (1961). It is shown that the error of the new method is 200 times less than that of Hajj and about 2500 times less than that of Cooley.