 How to Find the Second-Order Corrections to Energy Levels and Wave Functions - dummies

# How to Find the Second-Order Corrections to Energy Levels and Wave Functions

In quantum physics, in order to find the second-order corrections to energy levels and wave functions of a perturbed system, En, you need to calculate E(2)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: From the jumbo equation, you can then find the second-order corrections to the energy levels and the wave functions. To find E(2)n, multiply both sides of This looks like a tough equation until you realize that is equal to zero, so you get Because is also equal to zero, and again neglecting the first term, you get E(2)n is just a number, so you have And of course, because you have Note that if is an eigenstate of W, the second-order correction equals zero.

Okay, so How can you make that simpler? Well, from using Substituting that equation into gives you Now you have Here’s the total energy with the first- and second-order corrections: So from this equation, you can say That gives you the first- and second-order corrections to the energy, according to perturbation theory.