This is why you have to read Landau:
"In the limit of small velocities, the particle must be described, as in the non-relativistic theory, by a single two-component spinor: on taking the limit $\vec{p} \rightarrow 0$ we find $\zeta = \eta$, so that the two spinors which form the bispinor are equal. This, however, reveals a defect of the spinor form of Dirac's equation: in the limit, all four components of $\psi$ are non-zero, although only two of them are really independent. A more convenient representation is one in which two of it's components are zero in the limit."

@Acuriousimind Q3. After I found your answer on PSE to Q2 on 1:1 correspondance on hamiltonian to potentials (which is false because there exists isopsectral potentials). I am trying to model this scenario in the Quantum Moves game. However I am not sure how to model it because I cannot use perturbation theory because the potential will be changing quicker than the time dependence of the wavefunction.

Do I simply use some kind of born oppenhenier approximation and assume the wavefunction does not get changed by the potential well being translated quickly to the right side in order to compl…

They are currents due to the magnitisation of the material, If you have a bunch of magnetic dipoles in the material it can be distributed evenly or unevenly

Each magnetic dipole can be dscribed by a current loop due to ampere law.

Now similar to green's theorem, current loops can be added up and thus all the interior loops will be cancelled, leaving behind an overall surface current $\vec{K}$ loop that described the overall dipole moment due to all these dipole moments. If your magnetisation is not even, such as there are places where the dipoles are concentrated (the divergence is non ze…

@acuriousmind @JohnRennie (This is basically a state transition problem thus you might also be able to help)
https://i.sstatic.net/Abyq3.png
Let me elaborate. So the scenario is that there's a 1D potential well with a parabolic shape, and then inside there's an atom described by a probability distribution that is bimodal. The task is to move your potential well and adjust its depth in a way so that this bimodal wavefuntion become unimodal. Once you start moving the well, the probability distribution will start to slosh back and forth like a liquid

@ACuriousMind
I always thought I can somehow approximate the scenario since that's what we physicists do all the time in modelling a scenario by making simplification

For that one, my naive intuition was suggesting that analogous to how when you have a bowl of sloshing liquid when you jut the bowl to the left while the liquid is sloshed to the right, then you get a bowl of liquid that is more stationary because the movement of the bowl counters the direction the liquid is sloshing to.

however because this is quantum, I suspect I would need to do the maths to check whether the naive intuit…

@Acuriousmind EDIT: Ok I found the algorithm data from the nature article http://www.nature.com/nature/journal/v532/n7598/full/nature17620.html. The potential in dimensionless units is a gaussian potential $V_{tweezer}=\mathcal{A}exp(-\frac{2.0 (x-x_0)^2}{w_0^2})$ where $w_0$ is the waist and $\mathcal{A}$ is the depth. The time dependent schroedinger equation is then solved using the split step method (by treating the nonlinear and linear part of it as independent, solve them separately in the frequency domain and then fourier transform them back into the time domain)

@vzn I think I wrote clearer than my old messages for that one, perhaps since you and JR are somewhat more align to my thought process, you two might be able to translate to ACM?

Also remeber that we don't know the existence of that paper when we said about young modulus not defined for spacetime, JR does not need t be blamed for that

@ACM
But anyway, the question now evolve into a simpler one.

So basically after all that searching, I figure that the initial state is the 1st excited eigenstate of the gaussian potential, and the sloashing around is a superposition of some eigenstate of th…

@ACuriousMind Ok the question boils down to this. The potential they are using is the gaussian well

The initial state is the 1st excited state wavefunction. During the mouseclicking which changed the well's depth and width, the wavefunction evolves into a superposition of eigenstates (in a way such that the probability distribution obtained is similar as if the original wavefunction get sloshed around in the well)

After moving the potential sharply to the right, the wavefunction take the shape that is identical to the ground state wavefunction.