add comments to hamiltonian test

[marwahaha]

I tried to add some comments and fix the test. But nothing I tried seemed to work.

What I noticed:

1. The norms of qoH and H are always the same, but the difference has usually a large norm.
2. Both objects are Hermitian.
3. There's a weird sqrt(3) floating around in one of the modes; why?
4. I tried playing with the timescale but didn't notice it improving the issue.
5. I think the ion's level is labeled wrong ("D5/2", -1/2) -> ("D5/2", -5/2) but it didn't seem to improve the issue
6. Sometimes delta, phi, Omega are negative; is that ok?
7. I relabeled the ions for clarity.

Maybe something more fundamental is broken.

[jbroz11]

1. This means that the phases aren't consistent. (That's why we check the norm of the difference and not the difference of the norms). This is concerning, something must have broke, presumably around the time the split species was implemented (Do you have any idea what could be going wrong @neil-glikin ?)
3. This comes from the normal mode structure. The vibrational frequency of the "stretch mode" is sqrt(3) times larger than the center-of-mass mode (assuming identical masses).
4. timescale shouldn't change anything. so that's good. ... out of time for now

[jbroz11]

5. Both are allowed transitions, so this doesn't matter.
6. this is necessary for delta and phi, for omega it doesn't hurt

[neil-glikin]

Yeah I guess it must be the phases. If it happened from split-species then it must be from the electronic part. So it might be easy to check by trying with a super simple 2-level Hamiltonian with no motional degrees so freedom, so that there is essentially only one (off-diagonal) matrix element to compare between the IonSim construction and the manual construction. I unfortunately won't be able to work on it the rest of this week though :(

[marwahaha]

I tried playing around some more but I'm not sure how to generate the Hamiltonian you mention Neil.

[neil-glikin]

I found the problem; it was with the test. The way that the laser wavelength was defined needed to be changed from how it had been defined pre-split-species, but I hadn't done that properly. This resulted in the parameter $\Delta$ not actually reflecting the real detuning, and hence a disagreement in phases in the manually- and IonSim-constructed Hamiltonians.

For some reason I was only able to get this fix to work on the master branch, so I pushed that as well. To fix-h-test, I've pushed what I would think would be the same thing, but for some reason the test fails. I like @marwahaha's added comments and changes for readability so it would be nice to still incorporate them, but something functional must have changed as well that I haven't figured out.

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Codecov Report

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[marwahaha]

@neil-glikin is there a way to make IonSim error with that kind of input? It feels like we should prevent people from making this particular mistake.

I've updated this PR, it's ready to go after a review from either of you.

[neil-glikin]

@marwahaha We could, but I actually made it intentional that transitionwavelength can accept energy levels rather than sublevels as input, since it still makes physical sense to ask what is the energy difference. I think the mistake came from me hastily translating from the old syntax to the new. I could see the argument for this being a mistake that's too easy to make, though.

[marwahaha]

ok, that makes sense; sublevel transitions are different than level transitions. I think if even we can make the mistake, users will very likely make it.