Category: Quantum Wave Mechanics

It is interesting to note that Werner Heisenberg was working on his own quantum mechanics at the same time Schroedinger was coming up with his equation. In fact, together with colleagues Max Born and Pascual Jordan, Heisenberg actually developed and published his theory a short time before Schroedinger. This alternative theory was based on the… Continue reading Heisenberg’s Matrix Mechanics

What the Schroedinger theory doesn’t do is provide us with a physical interpretation for the value of the wave function Ψ at any particular location and time. Because it involves imaginary numbers, we can’t expect to assign any measurable property to Ψ anyway, so maybe it is just as well. Wave functions can be deduced… Continue reading Probability and Expectation Values

So far, this could be just a bunch of abstract math. These rules apply to any differential equation of the kind we are discussing. But we are interested in what is physically represented by the quantities in the equation. Well, as we’ve already alluded, Schroedinger was able to show that the right side of his… Continue reading Eigenfunctions, Eigenvalues, and Quantization

The funny thing about a differential equation (including the Schroedinger equation) is that its solution is, in and of itself, another equation. For example, the differential equation for the position of a macroscopic object that is moving in one dimension looks like this: . Here x(t) is the object’s position at time t, a represents how much the object is… Continue reading Solving the Schroedinger Equation

Schroedinger’s wave equation is sometimes just called the “wave equation” in quantum mechanics. This can be a source of confusion, because a wave function itself will look like an equation when we write it down. But the Schroedinger wave equation is a very special kind of equation called a differential equation. We know this because… Continue reading Wave Functions and the Wave Equation

The missing link in our picture so far is some way to determine the dynamic behavior of particle/waves like electrons, protons, and neutrons. Recall that in order to understand dynamic behavior–that is, how things move and change with time–we need to factor in the impact of forces. Newton’s laws of motion tell us how classical particles… Continue reading The Schroedinger Equation

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… Continue reading Introduction