Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

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.

share|improve this question
    
Intensities are the squares of amplitudes. They are definitely not the same thing. –  Michael Brown Apr 6 '13 at 5:44
4  
This is basically the physics version of the Freshman's dream! –  zkf Apr 6 '13 at 7:20
add comment

1 Answer

up vote 5 down vote accepted

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.

Besides, intensities are positive; you'd never get the chance for destructive interference if you were only superposing intensities.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.