Studying Quantum Mechanics I only thought about Spherical Harmonics $Y_{l,m}(\theta , \phi)$: $$Y_{l,m}(\theta , \phi)=N_{l,m}P_{l,m}(\theta)e^{im\phi}$$ as the simultaneous eigenfunctions of $L_z$ and $L^2$. But then I stumbled on these two statements: The Spherical Harmonics are a complete ort...

We are trying to create a custom pan flute. With some searching, we found a formula relating the length of a closed cylinder with the frequency at which it resonates, namely L = c / 4f, with c being the speed of sound. Based on this, we calculated that a cylinder to produce 880 Hz, or A5, would n...

Let us suppose that a fluid is flowing through a pipe (fully filled) of uniform cross section. The fluid is ideal and hence must flow in a streamlined path and must be in a steady state. This means that the path of particles of fluid must never intersect (streamlined flow) and hence the velocity ...

I understand that light of 100nm or less can cause an electron to be ejected from an atom, creating an ion. Could it instead cause a proton to be ejected from the atom? (This would also be "ionizing") Does it matter whether the atom is stable? If an atom is already an ion, does anything happen di...