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How to Find the Energy of a Perturbed System Based on the Wavelength Parameter

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

Then add the first-order correction to the energy,

image1.png

and add the second-order correction to the energy,

image2.png

Now what about the wave function of the perturbed system,

image3.png

Start with the wave function of the unperturbed system,

image4.png

Add to it the first-order correction,

image5.png

And then add to that the second-order correction to the wave function,

image6.png

Note that when

image7.png

becomes the unperturbed energy:

image8.png

and

image9.png

becomes the unperturbed wave function:

image10.png

So your task is to calculate E(1)n and E(2)n, as well as

image11.png

So how do you do that in general? Time to start slinging some math. You start with three perturbed equations:

image12.png

You then combine these three equations to get this jumbo equation:

image13.png
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