Schwinger variational principle for bound states and scattering problems

C. L. Dolph, Robert K. Ritt

Radosław Szmytkowski

Francisco Antônio Bezerra Coutinho

W. Lucht

Eberhard K. U. Gross, Erich Runge

We present a sequence of variational principles for scattering problems consisting of functionals of fractional form. Schwinger's variational principle and the functional recently proposed by Takatsuka and McKoy are discussed as special cases. For high scattering energies a correspondence to the Born series is established.

G. H. Goedecke, E. Brown

Potential scattering is treated by a minimum variational principle. The method, known as the error method, is applicable to problems which can be cast as linear inhomogeneous equations. The method makes use of a non-negative functional which reduces to zero for the exact solution. The magnitude of the functional for approximate solutions provides an indication of the accuracy of the wave function. The method is illustrated by some examples, and compared with the Schwinger and Kohn principles.