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The Lippman-Schwinger equation for two-nucleon scattering

The equation ϕm|ˆT|ϕn=ϕm|ˆV|ϕn+ϕm|ˆV1(EnˆH0)ˆT|ϕn, is called the Lippman-Schwinger equation. Inserting the completeness relation 1=n|ϕnϕn|,ϕn|ϕn=δn,n we have ϕm|ˆT|ϕn=ϕm|ˆV|ϕn+kϕm|ˆV|ϕk1(Enωk)ϕk|ˆT|ϕn, which is (when we specify the state |ϕn) an integral equation that can actually be solved by matrix inversion easily! The unknown quantity is the T-matrix.