# Chapter 11

# Giving Systems a Push: Perturbation Theory

In This Chapter

- Nondegenerate and degenerate perturbation theory
- Perturbing harmonic oscillators
- The Stark effect and perturbing hydrogen atoms

Problems in quantum physics can become pretty tough pretty fast — another way of saying that, unfortunately, you just can't find exact solutions to many quantum physics problems. This is particularly the case when you merge two kinds of systems. For example, you may know all about how square wells work and all about how electrons in magnetic fields work, but what if you combine the two? The wave functions of each system, which you know exactly, are no longer applicable — you need some sort of mix instead.

Perturbation theory to the rescue! This theory lets you handle mixes of situations, as long as the interference isn't too strong. In this chapter, you explore time-independent perturbation theory and degenerate and nondegenerate Hamiltonians. You also look at some examples that place harmonic oscillators and hydrogen atoms in electric fields.

## Introducing Time-Independent Perturbation Theory

The idea behind time-independent perturbation theory is that you start with a known system — one whose wave functions you know and whose energy levels you know. Everything is all set up to this point. Then some new stimulus — a *perturbation* — comes along, disturbing the status quo. For example, ...