Suppose a particle travelled one dimensionally. Classically, the particle’s behavior should be in line with Newton’s laws of motion. Quantum mechanically, however, one cannot determine the exact position and momentum of the particle and as such is reduced to using a probabilistic interpretation. Here we will explore the notion of a probability density and how one could derive such an artifact from a simple Taylor expansion argument. Continue reading Probability Densities in Quantum Theory
Here is a cute trick to derive the momentum operator in quantum mechanics. Usually, we taken this for a given or a definition, however there are ways to prove the relationship. Here we explore the relationship between position and momentum using Fourier Transforms.