# How to Normalize the Wave Function in a Box Potential

In your quantum physics course, you may be asked to normalize the wave function in a box potential. Here's an example: consider the wave function

In the *x* dimension, you have this for the wave equation:

So the wave function is a sine wave, going to zero at *x* = 0 and *x *= L* _{z}*. You can also insist that the wave function be normalized, like this:

By normalizing the wave function, you can solve for the unknown constant A. Substituting for X(*x*) in the equation gives you the following:

Therefore,

which means you can solve for A:

Great, now you have the constant A, so you can get X(*x*):

Now get

You can divide the wave function into three parts:

By analogy with X(*x*), you can find Y(*y*) and Z(*z*):

So

equals the following:

That's a pretty long wave function. In fact, when you're dealing with a box potential, the energy looks like this: