In quantum physics, in order to find the energy of a perturbed system, En, you need to start by calculating the energy and wave function of an unperturbed system. You start with the energy:
![image0.png](https://www.dummies.com/wp-content/uploads/398082.image0.png)
Then add the first-order correction to the energy,
![image1.png](https://www.dummies.com/wp-content/uploads/398083.image1.png)
and add the second-order correction to the energy,
![image2.png](https://www.dummies.com/wp-content/uploads/398084.image2.png)
Now what about the wave function of the perturbed system,
![image3.png](https://www.dummies.com/wp-content/uploads/398085.image3.png)
Start with the wave function of the unperturbed system,
![image4.png](https://www.dummies.com/wp-content/uploads/398086.image4.png)
Add to it the first-order correction,
![image5.png](https://www.dummies.com/wp-content/uploads/398087.image5.png)
And then add to that the second-order correction to the wave function,
![image6.png](https://www.dummies.com/wp-content/uploads/398088.image6.png)
Note that when
![image7.png](https://www.dummies.com/wp-content/uploads/398089.image7.png)
becomes the unperturbed energy:
![image8.png](https://www.dummies.com/wp-content/uploads/398090.image8.png)
and
![image9.png](https://www.dummies.com/wp-content/uploads/398091.image9.png)
becomes the unperturbed wave function:
![image10.png](https://www.dummies.com/wp-content/uploads/398092.image10.png)
So your task is to calculate E(1)n and E(2)n, as well as
![image11.png](https://www.dummies.com/wp-content/uploads/398093.image11.png)
So how do you do that in general? Time to start slinging some math. You start with three perturbed equations:
![image12.png](https://www.dummies.com/wp-content/uploads/398094.image12.png)
You then combine these three equations to get this jumbo equation:
![image13.png](https://www.dummies.com/wp-content/uploads/398095.image13.png)