When are asked about why an electron cannot fall into the nucleus we put together the argument that: as Heisenberg's uncertainty principle says $\Delta x \Delta p$ $\geq \frac{h}{4 \pi}$ $\Delta x \Delta v$ $\geq \frac{h}{4 \pi m}$ now we say that "as the size of the nucleus is 2fm(diameter)" $\D...

Statistical Mechanics setup: Consider a box of gas with $N$ particles in some initial macro state (fixed temperature, energy, etc.). A configuration of particles giving a fixed macro state is called a micro state corresponding to that macro state, and the set of all micro states is called the pha...

In my university, my professor said that every degeneracy in QM comes from a symmetry of the Hamiltonian. But I'm not sure it is true for all the cases. My counter-example is as follows: In the 3D harmonic oscillator, $E_n=\hbar\omega(n+m+l+3/2)$, where $(n,m,l)$ are quantum numbers of $x,y,z$ os...

I have a follow up question for What do the stars really look like, if you could travel at almost lightspeed? If we are on a spaceship, travelling at a constant speed of 99.999% the speed of light, most of the stars I see on one side will be blue-shifted. And most of the stars on the other side w...