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HNQ
6:27 AM
5
Q: Behavior of a loose coin on a free fall ride

the_photonAt 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…
HNQ
11:11 AM
1
Q: Operators and their Eigenstates in Quantum Mechanics

Anti-TachyonSuppose 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…
HNQ
7:46 PM
1
Q: Number of Independent Components of Levi-Civita Christoffel Symbol

Math noobCan 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…
HNQ
10:21 PM
5
Q: Why do we hear frequencies in the basis of sine waves?

interoceptionWhen 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...

 

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