 Solution

Let $U_s=U(y_s)$ at an inflection point supplied by the preceding identity. Its imaginary part, divided by nonzero $c_i$, gives $\int U^{\prime \prime }|\psi {|}^2/|U-c{|}^{2}dy=0$. Its real part isAdding $(c_r-U_s)$ times the zero integral replaces $U-c_r$ by $U-U_s$:Therefore the integrand's profile factor must be strictly negative somewhere in the open channel:This is the Fjørtoft theorem. The positive weight and the strictly negative integral establish the strict inequality, not merely a nonpositive value. It is a stronger necessary condition than Rayleigh's inflection-point theorem, and neither condition alone proves instability.