In the Dirac notation, the wave equation can be written as an inhomogeneous equation, ( E − − H 0 ) | ψ ψ ⟩ = V | ψ ψ ⟩ , where H 0 is the kinetic energy operator. The solution of the homogeneous equation is | ϕ ϕ ⟩ , where ( E − − H 0 ) | ϕ ϕ ⟩ = 0 . A formal solution of the inhomogeneous equation is the sum of the solution of the homogeneous equation with a particular solution of the inhomogeneous equation | ψ ψ ⟩ = | ϕ ϕ ⟩ + G 0 + V | ψ ψ ⟩ , where G 0 + = lim ε ε → → 0 ( E − − H 0 + i ε ε ) − − 1 . This is the Lippmann–Schwinger equation, which can also be written | ψ ψ ⟩ = ( 1 + G 0 + T ) | ϕ ϕ ⟩ . The t-matrix is defined by T = V + V G 0 + V + V G 0 + V G 0 + V + . . . .