I recently asked a question about why relativistic effects come into play only with the superheavy elements. The top answer I got was pretty good and I understand most of it, but the answer brought up another question for me. The answerer said that the electrons move around their orbitals at .58c...

I've been casually reading up on Hamiltonian Mechanics and integrable systems and one term that is used a lot of "invariant torus" where bounded orbits live. KAM theory is also mentioned as the reason why. Upon searching up the wiki page for Action-Angle Variables I encounter this line: Action-a...

I do know that there are at least two types of yellow light: a light of a single wavelength of ~580 nm and a combination of green light and red light. (Technically, there could be more yellow light.) And the following two figures are making me confused. Are red and green light reflected from ba...

The Gross-Pitaevskii equation admits soliton solutions such as: $$\psi(x)=\psi_0 \tanh(x/\xi),$$ where $\xi$ is the healing length defined by: $\xi=\frac{\hbar}{\sqrt{m \mu}}$, with $\mu$ being the chemical potential. To obtain this solution, one of the boundary conditions is given by assuming th...

In my study of general relativity, I came across tensors. First, I realized that vectors (and covectors and tensors) are objects whose components transform in a certain way (such that the underlying reality is one and observers in different reference systems observe the same thing differently). T...