At Six Flags over Texas, there used to be a free-fall drop ride called "the cliffhanger". Simply put, you got into a metal box, got elevated up to about 75 feet or so, and got dropped straight down. One of the things riders would sometimes do is, while seated in the car, place a penny or coin on...

Suppose that a quantum state $|\Psi\rangle$ is given by $|\Psi\rangle = \Sigma_{i=1}^{n}\alpha_{i}|\psi_{i}\rangle$, where each $|\psi_{i}\rangle$ is an eigenstate of an operator $M$ and $\sum_i\vert \alpha_i\vert^2=1$. Generally, $|\Psi\rangle$ would not be an eigenstate of $M$ for $n>1$. Then h...

When we talk about hearing frequencies and overtones, we almost always mean in the basis of sine waves, according to a standard Fourier decomposition. Couldn't we also decompose a signal into a different basis of orthogonal periodic functions, like square waves? According to a Fourier decompositi...