Solution of the Schrödinger equation containing a Perey–Buck nonlocality

The solution of a radial Schrödinger equation for image containing a nonlocal potential of the form image 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 image and image is obtained, depending on the number of polynomials employed. The second method consists in expanding ψ into a set of image Sturmian functions of positive energy, supplemented by an iteration procedure. For image an accuracy of image is obtained without iterations. After one iteration the accuracy is increased to image. 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.