How Does L1.1 General problem. Non-degenerate perturbation theory Work?

Imagine you're trying to solve a puzzle, but someone gently changes one piece just enough to make it slightly harder, that’s non-degenerate perturbation theory in action.

You start with a simple problem, like solving a basic math equation or figuring out how far a toy car will roll. This is your original system, and you know exactly what the answer is. Now, imagine someone adds a tiny bump to the road, not enough to stop the car completely, but just enough to make it take a slightly different path. That’s like adding a small change or perturbation.

In non-degenerate perturbation theory, we use this idea to solve problems that are almost like the ones we already know how to solve, but with a tiny twist. It's like having a favorite recipe, and then just adding a pinch of salt instead of sugar, still tasty, but slightly different.

Think about your favorite puzzle again. You know all the pieces by heart. Now, someone moves one piece just a little bit, not enough to confuse you completely, but enough to make the whole picture look just a bit different. That’s how non-degenerate perturbation theory works: it helps us find new answers when things are almost like what we already know.