#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.

[parasocial-paradox]

"Heart-eyes Howell" actually common misconception. Dan perceives the audience and/or real human faces via refraction [1] off the Phil, who effectively functions as a wireless conduit for his thoughts, paradoxically dampening intelligence via blonde photo-resistor and amplifying homosexual signals through the mirrored perception of the self. [2]

References: [1] one-quarter of an engineering degree

[2] trust me bro

[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

[rubenesque-as-fuck]

Turns out getting laid is also great for my executive function. Who knew the boardroom just needed some backshots to get shit done

[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]

[langernameohnebedeutung]

we are well over a decade past that point but that's also precisely why (overton window) i feel the need to say - - - for people in a modern democracy to vote signature red hats with a slogan on it like some sort of uniform/group identifier is plenty fucking weird.

[dosesofcommonsense]

[arcanegifs]

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

[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

[underthehedge]

I'm having A Thought about cultural assumptions and how people often conflate their own cultural quirks and patterns as being either universal or Obviously Logical, based on seeing a post with someone's lock screen, because I have ADHD.

It was a simple example but a very neat one, and it's about how we write and speak about dates (as in the measure of time, not the fruit of the date palm or an intimate meeting). Americans write dates backwards, by the standards of nearly every culture (inc. other English speaking cultures). They write them MM/DD/YY instead of DD/MM/YY, this is known.

But the thing is, ok there is a good reason most people write the day then month but none the less, what a culture decides on is still just a little bit arbitrary, the point is it's a cultural agreement that This Is How It's Done. Earlier I saw a post with someone's lock screen, an American, and it displayed something like "Wednesday, December 12" and that caught my eye because mine obviously reads "Thursday, 9 March", because I come from the UK, where we use DD/MM.

And I was reminded of an American once telling me how MM/DD obviously makes more sense though, because you see, that's how you say dates in English! You would say "March ninth", so you write the month then the day! Except, well, that's not how we say dates here, we say "the ninth of March". But this guy had assumed that the standard phrasing in his culture was just how all English speakers would say it, therefore the date format they used was clearly the more natural and intuitive way, and of course you think in terms of the month something is happening and then when in the month it is!

To me, however, this feels like someone earnestly and confidently explaining that naturally you put your socks on over your shoes.

Obviously there's a bunch of examples of this kind of thing, and many with far greater importance, but it just seemed like a really very telling and concise example of how people will see features of their culture that result from specific quirks as universalities that make more sense than any other system.

[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