Ever heard of the term “wave function” in relation to quantum mechanics? What does it mean? How is it interpreted?

Hey everyone, I’m back with a new video! This time, we’re going back to basics and understanding exactly what a wave function is, as well as what it represents, in the world of quantum physics. This video is going to be the first in a series I’m going to call “Quantum Mechanics… But Quickly”. In this series, I want to discuss some fundamental quantum concepts, and explain them in as visual and intuitive a way as possible – without having to sit through an hour long lecture, or understanding complicated graduate level mathematics.

A physicist named Louis de Broglie once suggested something amazing. While scientists were busy debating whether light was a wave or a particle, de Broglie suggested that even matter – things with mass (e.g. electrons, protons, atoms, etc.) – could behave like waves. This idea was revolutionary due to the mountains of evidence scientists had up until that point that matter behaved like particles. However, the quantum world was soon to revolutionise everything we thought we knew about the universe. And as it turns out, de Broglie’s suggestion was right.

His suggestion of matter waves permeated into the work of Erwin Schrodinger. Combining the idea of matter waves with the principle of Conservation of Energy, Schrodinger came up with the equation we now know as the Schrodinger Equation. This ended up being the governing equation of quantum mechanics, and crucially contained a function known as the wave function. This wave function contained mathematical information about any quantum system we happened to be studying.

The key question, then, was about what the wave function actually related to. What did it correspond to in real life? How should we interpret it? Well, there are a few different interpretations of quantum mechanics and how it relates to our real-life universe. The most commonly accepted one is the Copenhagen interpretation. And this interpretation suggests that a wave function is directly related to the probability distribution of a system. Specifically, if we take a system’s wave function and square it (well, technically if we take its square modulus), then this will give us the probabilities of various results occurring when we make a measurement on a system. For example, the wave function of a system could tell us the probability of finding a particle at a certain position in space. Or it could tell us the probabilities of finding different spin states when measuring the spin of an electron, for example.

In this video, we discuss these examples in detail. Additionally, we briefly look at the consequences of wave functions having imaginary parts. Lastly, we look at how the Schrodinger Equation (or at least the time dependent Schrodinger Equation) governs how a wave function changes over time – apart from when we make a measurement on the system. This measurement causes a discontinuous and jarring change in the wave function, known as the “collapse of the wave function”. This collapse has caused many philosophical problems for physicists over the years, and it continues to do so to this day.