 Neumann spectral formula for half-line constant drift

The reflected global relation expresses the unknown value trace in terms of the prescribed derivative trace. Multiplying the half-line drift null contour identity by $(ik+\alpha )/(ik)$ removes the reflected time-dependent transform. Its pole at $k=0$ lies below the contour and is not crossed. The formula concerns the derivative $q_x(0,t)$, rather than the outward derivative $-q_x(0,t)$.