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 development of the variational formulation of the scattering theory can be traced to works of L. Hultén and J. Schwinger in 1940s.
[1] The T-matrix expressed in the form of stationary value of the functional reads where
is the retarded Green's operator for collision energy
satisfy the Lippmann-Schwinger equation and Different form of the stationary principle for T-matrix reads The wave functions
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
is guessed, with some free parameters, that are determined from the condition of stationarity of the functional.