Schwinger variational principle is a variational principle which expresses the scattering T-matrix as a functional depending on two unknown wave functions. The functional attains stationary value equal to actual scattering T-matrix. The functional is stationary if and only if the two functions satisfy the Lippmann-Schwinger equation. The development of the variational formulation of the scattering theory can be traced to works of L. Hultén and J. Schwinger in 1940s.
Contents
Linear form of the functional
The T-matrix expressed in the form of stationary value of the functional reads
where
and
Fractional form of the functional
Different form of the stationary principle for T-matrix reads
The wave functions
Application of the principle
The principle may be used for the calculation of the scattering amplitude in the similar way like the variational principle for bound states, i.e. the form of the wave functions