6:27 AM
5

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...

5 hours later…
11:11 AM
1

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...

9 hours later…
7:46 PM
1

Can anybody explain why Levi-Civita Christoffel symbol in general $N$ dimensional space have $\frac{N^2(N+1)}{2}$ independent components? I have read that in $N$-dimensional space, metric tensor has at most $\frac{N(N+1)}{2}$ independent components and for each component we can have $N$ independe...

3 hours later…
10:21 PM
5

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...