where | χ χ ⟩ ⟩ is a wave function like Lagrange multiplier and the λ λ parameter regulates the integral intensity. Variation of J ′ with respect to δ δ ϵ ϵ and δ δ ψ ψ leads to two coupled Schrödinger equations. A forward equation for | ψ ψ ⟩ ⟩ with initial condition | ψ ψ ( 0 ) ⟩ ⟩ = | ϕ ϕ i ⟩ ⟩ and a backward equation for the Lagrange multiplier | χ χ ⟩ ⟩ with final condition | χ χ ( T ) ⟩ ⟩ = | ϕ ϕ f ⟩ ⟩ . Finding a solution requires an iterative approach. Different algorithms have been applied for obtaining the control field such as the Krotov method.