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
![image0.png](https://www.dummies.com/wp-content/uploads/396998.image0.png)
In the x dimension, you have this for the wave equation:
![image1.png](https://www.dummies.com/wp-content/uploads/396999.image1.png)
So the wave function is a sine wave, going to zero at x = 0 and x = Lz. You can also insist that the wave function be normalized, like this:
![image2.png](https://www.dummies.com/wp-content/uploads/397000.image2.png)
By normalizing the wave function, you can solve for the unknown constant A. Substituting for X(x) in the equation gives you the following:
![image3.png](https://www.dummies.com/wp-content/uploads/397001.image3.png)
Therefore,
![image4.png](https://www.dummies.com/wp-content/uploads/397002.image4.png)
which means you can solve for A:
![image5.png](https://www.dummies.com/wp-content/uploads/397003.image5.png)
Great, now you have the constant A, so you can get X(x):
![image6.png](https://www.dummies.com/wp-content/uploads/397004.image6.png)
Now get
![image7.png](https://www.dummies.com/wp-content/uploads/397005.image7.png)
You can divide the wave function into three parts:
![image8.png](https://www.dummies.com/wp-content/uploads/397006.image8.png)
By analogy with X(x), you can find Y(y) and Z(z):
![image9.png](https://www.dummies.com/wp-content/uploads/397007.image9.png)
So
![image10.png](https://www.dummies.com/wp-content/uploads/397008.image10.png)
equals the following:
![image11.png](https://www.dummies.com/wp-content/uploads/397009.image11.png)
That's a pretty long wave function. In fact, when you're dealing with a box potential, the energy looks like this:
![image12.png](https://www.dummies.com/wp-content/uploads/397010.image12.png)