# Can we use intensities in the superposition principle?

In using the superposition principle to calculate intensities in interference patterns, can we add the intensities of the waves instead of their amplitudes? I think that amplitude account for the intensities so that both are the same thing and so it doesn't matter.

-
Intensities are the squares of amplitudes. They are definitely not the same thing. – Michael Brown Apr 6 '13 at 5:44
This is basically the physics version of the Freshman's dream! – zkf Apr 6 '13 at 7:20

No, it is amplitude. Amplitude is $\Psi$, intensity is $|\Psi| ^2$.
Schrödinger's equation (where $\hat H$ is linear) is: $$\hat H\,\Psi=E\,\Psi.$$ So, if you have two possible states $\Psi_1,\Psi_2$, then $$\hat H\,\Psi_1=E\,\Psi_1,\\\hat H\,\Psi_2=E\,\Psi_2.$$
We can add these and get $$\hat H (\Psi_1+\Psi_2)=E(\Psi_2+\Psi_2).$$
This shows us that the superposition of amplitudes still satisfies Schrödinger's wave equation. On the other hand, there is no guarantee that $\sqrt{\Psi_1^2+\Psi_2^2}$ (the amplitude that you get if you superpose intensities) will satisfy the wave equation.