#wave functions

[dat-physics-gal]

Explain to me dipole selection rules please I beg

Okay, so for a transition between energy eigenstates, there needs to be an exchange of a photon with the correct energy. I'm assuming you know that.

Since photons are waves of the electromagnetic field, they impose an electric moment on charged particles, which in a vast majority of cases can be modeled as a simple dipole moment.

Now here's where the quantum mechanics starts: The dipole moment is expressed as a linear operator, which when applied to the wave function of a particular state gives you back the eigenvalue for the dipole moment of that state. However, since we want to describe the transition between states, and the operator only applies to the ket of the wave function, the bra and the ket which it is nestled in between are of the different states, aka the starting and the final electron state.

The operator applies to the starting state ket, which can then be completed on the left with the final state bra, and then integrated over to obtain the transition dipole moment integral.

This integral will tell you the expectation value for the transition. For the selection rules, you don't actually have to precisely calculate this integral, you just have to find out whether or not it is zero, because if it is, that means you have an impossible transition on your hands.

Depending on your representation, the dipole operator as well as the wave functions will look different, as will the space you integrate over.

So first, find which representation (spatial, spherical, momentum space, etc.) you are working with, how the dipole operator looks for that representation, and then pick the two states you want to see if a dipole transition exists between them.

The tricky part is usually to get the wave function representation right, and then to leverage the symmetries of that function to determine if the value of the integral is zero or not. The representation that i find most common for tasks like this is this one, which separates the wave function into a radial and two angular parts. It is also already conveniently expressed in terms of 3 quantum numbers, that being the main quantum number n, the orbital angular momentum number l, and the magnetic quantum number m.

I am afraid you'll have to learn the quirks and symmetries of the generalized Laguerre polynomials as well as the spherical harmonics, in order to make statements about the transition dipole moment integral. However, once you get a feel for their symmetries and remember in what special cases integrals vanish (like integrating an odd function over a symmetric interval, etc.) you will be able to derive the selection rules.

I know this wasn't a simple and easy answer, but, well, this is quantum mechanics, to be fair. Hope that helped anyway.

[likesdoodling]

Was listening to music after studying today, so I figured I'd draw some tiny maglors to round out the day :)

[sforzesco]

BALAK, PANGAGAD

uhhh conspiracy. can be a courtship dance. ritual. so to speak. & hosting one in your house is an act of service

[cosmicportal]

“Gravity is a response to geometry”

~Albert Einstein

[dosesofcommonsense]

[arcanegifs]

all of these arcane s2 teasers feel so overwhelming after having a content drought for like 3 years lmao

[pocket-sized-nightmare]

my chronic migraines have been a pain in the ass lately and i have had no energy for anything. however, i do love to project onto my blorbos. so consider, in the vein of my pearl-with-tourette's fic – pearl with bad ping helping out gem, who's in a temporary state of lag bad enough that falling blocks cause her to crash

now if only my body would cooperate with me long enough to write,

[fehck]

[d8tl55c]

as much as i crave (ava 11+) answers

there's a part of me that i think will miss this anxious not-knowing state. the itch that's fun to scratch in different ways. an empty stretch of canvas i tried to fill in different ways, but will ultimately be painted over by the truth

we're never gonna not know what happens ever again

[heavenuphere]

when there's post punk at the function 😁

[headless-robot]

I find it really funny Gregor has gotten two 3 star id's based on characters in story that you would expect to have dedicated boss fights against them but don't.

[gender-trash]

they should invent a going to protests that doesnt make you so so so overstimulated and exhausted

[kyliafanfiction]

I will never understand the 'Coil is simulating timelines' interpretation of his powers that people have (that Coil himself actually wonders about) because it fundamentally makes no sense. Even though Wildbow claims that's the official version.

Coil doesn't simulate the possible outcomes of a choice in the future and then pick the choice and do it. He makes the choice and runs both options simultaneously in real time and then picks the outcome he prefers.

If he's choosing between A and B, he doesn't, before picking, simulate if A or B is the better choice for him. He does both A and B, sees how they play out, at the same time, and then collapses whichever timeline he doesn't like.

It can't be a simulation of both or 'the other choice' or whatever, because once he collapses a timeline, the remaining one becomes the sole reality.

People seem to think simulation makes... more sense? I guess? But we're talking about the Wormverse here. Shards are absolute fucking BULLSHIT.

Wildbow's attempt to make this more... coherent, is the claim that one Coil picks a timeline, his body 'autopilots' him into doing his chosen outcome, but that sure doesn't fucking seem to be how his interlude is written. Nor does that make any sense with the power as described in canon and text.

I don't know why Wildbow chose this more convoluted path to how Coil's power works. He explicitly created Shards to be broken and nonsensical in the nightmare level insane shit they can do sometimes, and somehow parallel timelines is a step too far?

[dosesofcommonsense]

[fresherfriut]

[rozecrest]

i have been writing old woman yuri like my ass is lit on fire and gelphie is restwater lake since finishing out of oz