Quantum Physics For Dummies, Revised Edition
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In quantum physics, in order to find the first-order corrections to energy levels and wave functions of a perturbed system, En, you need to calculate E(1)n, as well as


So how do you do that? You start with three perturbed equations:


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


You can handle the jumbo equation by setting the coefficients of lambda on either side of the equal sign to each other. After matching the coefficients of lambda and simplifying, you can find the first-order correction to the energy, E(1)n, by multiplying


Then the first term can be neglected and you can use simplification to write the first-order energy perturbation as:


Swell, that's the expression you use for the first-order correction, E(1)n.

Now look into finding the first-order correction to the wave function,


You can multiply the wave-function equation by this next expression, which is equal to 1:


So you have


Note that the m = n term is zero because


So what is


You can find out by multiplying the first-order correction,


And substituting that into


gives you


Okay, that's your term for the first-order correction to the wave function,


The wave function looks like this, made up of zeroth-, first-, and second-order corrections:


Ignoring the second-order correction and substituting


in for the first-order correction gives you this for the wave function of the perturbed system, to the first order:


About This Article

This article is from the book:

About the book author:

Steven Holzner is an award-winning author of technical and science books (like Physics For Dummies and Differential Equations For Dummies). He graduated from MIT and did his PhD in physics at Cornell University, where he was on the teaching faculty for 10 years. He’s also been on the faculty of MIT. Steve also teaches corporate groups around the country.

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