We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A-amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m-function associated with the Schrödinger operator H = -∂_x ² + q(x) on L ₂(0, ∞) with Dirichlet boundary condition at x = 0.