A canonical approach for computing the eigenvalues of the Schrodinger equation for double-well potentials

AThe problem of obtaining the eigenvalues of the Schrodinger equation for a doublewell potenthil function is considered. By replacing the differential Schrodinger equation by a Vollerra integral equation the wave function will be given by (psi)v= sigma =0 ai fi where Athe coefficients ai are oblained from the boundary conditions and the fi, are two well-defined canonical functions. Using these canonical functions, we deline an eigenvalue function F(E) = 0: its roots E1, E2. ... are the eigenvalues of the corresponding double-well potential. The numerical application to analytical potentials (either symmetric or asymmetric) and to a numerical potential of the (2)ʹ sigma state of the molecule Na2 shows the validity and the high accuracy of the present formulation.