Solution of the Schrödinger equation containing a Perey–Buck nonlocality

The solution of a radial Schrödinger equation for ψ(r) containing a nonlocal potential of the form is obtained to high accuracy by means of two methods. An application to the Perey–Buck nonlocality is presented, without using a local equivalent representation. The first method consists in expanding ψ in a set of Chebyshev polynomials, and solving the matrix equation for the expansion coefficients numerically. An accuracy of between 1:10−5 and 1:10−11 is obtained, depending on the number of polynomials employed. The second method consists in expanding ψ into a set of NS Sturmian functions of positive energy, supplemented by an iteration procedure. For NS=15 an accuracy of 1:10−4 is obtained without iterations. After one iteration the accuracy is increased to 1:10−6. Both methods are applicable to a general nonlocality K. The spectral method is less complex (requires less computing time) than the Sturmian method, but the latter can be very useful for certain applications.