Sign up ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Suppose you have 2 normalized wavefunctions $\psi_1=Ne^{iax}e^{if(x)}e^{i\omega t}$ and $\psi_2=Ne^{-iax}e^{if(x)}e^{i\omega t}$ defined on $x\in [-x_0,x_0]$ and vanishes for $|x|>x_0$. What then is the normalization factor for the superposed wavefunction? Perhaps an argument by the symmetry?

share|cite|improve this question

1 Answer 1

up vote 3 down vote accepted

$e^{i\theta} + e^{-i\theta}$ is just $2\cos \theta$. The superposed wavefunction is

$$\Psi(x,t) = 2N\cos(ax) e^{i(f(x) + \omega t)}$$


$$\Psi^*\Psi = 4N^2\cos^2(ax)$$

The average height is $2N^2$ if $x_0a = n\pi/2$, in which case $N = \frac{1}{2}\sqrt{1/x_0}$. Otherwise you can do this integral.

share|cite|improve this answer
Note: f(x) is being assumed to be real value – Chris Kuklewicz Oct 15 '11 at 17:21
@Chris Yes, thank you. – Mark Eichenlaub Oct 15 '11 at 19:55

Your Answer


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.