Introduction

• The difference between a wave function and the wave equation
• Force fields described by potential energy functions
• How particle wave functions respond to forces
• The Schroedinger equation and its solution

We get into the real nitty-gritty of modern quantum physics. We will learn about the powerful equation that quantum physicists have come up with to describe how particles behave when they interact with other particles and forces. We’ll learn what this equation signifies, how it is solved, and what those solutions mean. Then, we’ll see how it naturally leads to all those postulates that seemed to have been plucked from thin air in earlier. Hang on to your hats—this is where it all comes together.

Before diving in, keep our ultimate goal in mind: we want to understand how the natural world works, how it is built from whatever it’s made of, and how it evolves with time. We’ve learned that all of the matter we are familiar with (including ourselves) is constructed from atoms. We want to know how electrons can be bound to nuclei in those atoms, then how those same electrons help atoms bind into molecules, metals, air, water, jelly beans, etc. That means we have to figure out how all of the basic subatomic wave/particles behave under the influence of forces. For this, we will need that special equation, which was first written down by Erwin Schroedinger.

This is a fundamental equation, on par with Newton’s laws of motion, and we’re going to have to show it to you in order to understand what it actually tells us. But don’t worry, we won’t go into all of the mathematical intricacies of its solution and we won’t actually do any math. We’ll introduce and describe and then see how it applies to some illustrative cases in the next.