Quantum mechanics is perhaps one of the more counter-intuitive fields in physics as it goes against our classical understanding of the physical world. However, not only is the physics quite bizarre, I believe the math is too when you first learn it. While in most other field of physics, the connection between the physics and the mathematics used tends to be relatively clear, when it comes quantum mechanics the connection is really not obvious. How can an area about abstract vector spaces and matrices have anything to do with the probabilistic nature of particles? Well there is actually quite a deep and eye-opening relation as we will see in this post.
This will definitely be one of my longer posts as it is impossible to get through everything in a short amount of time but if you are interested feel free to read until the end. Also, just as a prerequisite, throughout this post I will be assuming a high school level understanding of quantum mechanics and some understanding of linear algebra from vector spaces to eigenvectors.
The Wave Function
I think the best way to understand the intuition behind the math of quantum mechanics is to begin with the (position) wave function Ψ(x, t). The wave function can essentially be thought of as a mathematical way to represent the state of…
