 Local relation

A spectral-parameter-dependent divergence identity equivalent to a partial differential equation. Integrating it over a space-time region gives a global relation between transformed initial and boundary data. For the half-line free Schrödinger equation, take $P=e^{-ikx+i{k}^{2}t}q$ and $Q=e^{-ikx+i{k}^{2}t}(-kq+i{q}_x)$.