@dm__ can I ask a clarification on your WE question?

How familiar are you with coupling and recoupling of angular momenta, and how comfortable are you with composite tensors?

@ZeroTheHero hi there, sure thing. I'd say I'm moderately comfortable. understand well how to change basis using CG coefs, or just using lowering/raising to figure out the states. also feel pretty good using the WE thm., then proj. thm. As far as composite tensors, I feel just ok, not the best. for example, in determining the spherical tensor of $xy$, my approach is to rewrite x,y in spherical coords, rewrite that in terms of spherical harmonics, and then associate them to spherical tensors.

@dm__ Ok AFAIR the full answer involves composite tensors and $9j$ symbols. I don't have my notes handy ; I can fetch them and I can write it up but it will take a few days - it's real busy right now. You can adjust the general answer as require by your specific example.

@ZeroTheHero that would be immensely appreciated, if you happen to have the time. it has been my main source of confusion. @IamAStudent gave me some links to look at, so I'm gonna start familiarizing myself with those Wigner symbols. have my QM qual tomorrow, then EM, so it'll be a few days XD

The general answer is quite messy and basically $9j$ symbols were "invented" for the use of WE with composite tensors acting on different spaces - most prominently for the spin-orbit interaction. If your tensor actually acts in a single space - say spin or orbital part only - then the $9j$ collapses to something slightly more manageable - probably some $6j$ symbol but I need to look up the details. So all the "hard" part is hidden in the $9j$ or $6j$, which in practice one can look up.

anyways I'll get to this by end of week.

almost sounds like complicated mess that is the completely general equation to determine the CG coefs, but it's all hidden by writing it as $C_{l,m_l;s,m_s}^{j,m_j}$. and alright sounds great, I'm gonna get back to studying. cheers

clarification: not a mess, just an incredibly long expression :)

@dmckee hey... you were a teacher in a previous life...

Yeah.

How would you explain the following: take an ideal solenoid with a "slowly" varying current. The B-field is still $0$ outside, but uniform inside. How can this induce a current in a wire completely outside the solenoid, but which surrounds the solenoid? The field is $0$ at the location of the pick-up wire...

It's a 1st year physics problem... Haliday-Resnick...

but all the answers I can come up with are very much more complicated than 1st year physics... like hidden-momentum stuff.

I realize there is a flux through the surface defined by the pick-up wire due to the changing B in the solenoid, but there is still no field at any point on the pick up coil.

If one naively looks at the local relation $\nabla\times \vec E=\frac{\partial \vec B}{\partial t}$, $\vec B=0$ always at the pick-up coil... so you'd think $\vec E=0$ follow but maybe there's something funny in the boundary condition.

That's ... tricky. I'm not sure I have a good explanation at any level.

Haliday-Resnick solution is basically: close your eyes, just compute the flux through the surface defined by the pick-up loop, and use Faraday's law of induction from there.

but that's not very satisfactory.

I just can't seem to find any discussion of this...

^ I think that is the treatment in every intro book I know of. I"d love to bag on H&R (do it every chance I get because I really don't like that book), but I think they are firmly in line with the pack on this.

not even in Purcell...

yeah I hear you. I reference H&R because it's well known but all the others tow the same line.

Hmmm ... so we're increasing the current, and if the effect is generated by increasing a voltage elsewhere in the circuit then the increase is not by the same factor everywhere. You specified "slowly" but that means we have a smaller effect to explain just as much as a smaller lever to use in explaining it.

Pehaps we should be looking at the field due to a inhomogeneus but otherwise ideal solenoid?

well I want to keep the quasi-static approximation so that Biot-Savart still holds. Then either by Ampere or by integrating Biot-Savart the field in homogeneous inside the solenoid and completely contained in it.

if quasi static does not hold maybe there's some radiative effect...

but that would NOT be first year.

No. We're getting into graduate territory really fast. And while I did well in that class I have since forgotten almost everything I learned to survive Jackson.

I have a prepared a question on this... maybe I'll post it. It's just so weird I can't get to first base using some basic explanation.

BTW- I did well in the class because I felt so unprepared (every week of the term) that I put more time into it that all my other classes combined. I was not a natural.

:D

I know the feeling.

induction has some really subtle aspects...

I know there's some Am.J.Phys. by Griffiths on this hidden momentum stuff and on the homopolar generator...

I really important news: tonight's batch of chili seems to have come out well. I'll let the flavors meld over night and then huevos rancheros before work to start the day right.

you need cafe de olla with that!

I've actually never tried that. Must find some place around here that does it.

Major benefit of moving back to the desert is good Mexican cooking (well, what the US southwest has done with Mexican cooking, anyway) is easy to find again.

good cafe de olla is really good.

do you mind narrowing down which desert you hang around these days?

I'm south of Albuquerque. And to pin-point the matter for those familiar with the area, the rumble of occasional explosions across the town doesn't raise an eyebrow 'round here.

right... ok that's good enough.

@dmckee thanks for the feedback on the induction; I posted a question on this. I gotta go and prep for tomorrow.

Stack exchange is down huh

Can someone clarify the following for me please ( I am having a brain fart). For the classical Kepler problem you can have $U = \pm C/r$ For a potential $U$. But that means the Lagrangian can be either $L = v^2/2 \pm U$. Does this matter that depending on whether you choose the positive or negative sign you have a different Lagrangian?

@rob I know. That's part of what makes it funny.

I like your Agatha Christie idea...

@EmilioPisanty turns out that using $a$ and $a^*$ make that problem I was asking about way easier.

However, it comes at the cost of having to invoke the rotating wave approximation in a way that I feel is somewhat poorly justified.

Then again, I never did like the rotating wave approximation.

@ZeroTheHero quick question about a concrete selection example that will help me get the hang of this. curious about whether I can or can't rule out the element $\langle \alpha,j=1/2,m=1/2|(J_x^2-J_z^2)|\alpha,j=1/2,m=1/2\rangle$. I can rewrite that argument as a sum of $T_0^{(0)}, T_0^{(2), T_{-2}^{(2)}$, and $T_{2}^{(2)}$, so I think my selections are $\Delta m = 0,\pm2$, and $|\Delta j|\leq 2$, so I want to say that element is not necessarily zero.

omg.

that was a mess. missed a dollar sign and couldn't track it down, then something copy pasted. just disregard that whole thing.

what that was trying to layout was that $J_x^2-J_z^2$ can be rewritten in terms of $T_0^{(0)},T_0^{(2)},T_{-2}^{(2)}$, and $T_{2}^{(2)}$. so the selection rules would be $|\Delta m| = 0,\pm 2$, and $|\Delta j|\leq 2$, and this element would not necessarily be zero. is that correct?

sorry, no absolute value meant for that $\Delta m$

@JohnRennie hey John, really gotta get some rest right now, but if you feel so inclined, take a look at my post: physics.stackexchange.com/questions/467136/…. I feel like I'm missing something obvious, but I've been studying too much, and I'm confusing myself.

@dm__ your function is stationary in the sense that the coefficients $a_i$ in your superposition $\sum_i a_i \psi_i$ do not change with time.

The function is not time independent because the relative phases of the $\psi_i$ functions changes with time. For a nice demonstration of this see Emilio's answer here.

I suspect you've mixed up the meanings of stationary and time dependent. They are not mutually exclusive.

Hmm, OK, I mixed up the meaning of stationary as well. But my point still stands. Your function isn't stationary because its observables aren't time independent, but the coefficients $a_i$ are still time independent.

Slo day

@ZeroTheHero How is this any different from asking "a point charge makes an electric field at distant points. But at those points, div E is exactly zero. So how can E be nonzero?"

Like, I hope I'm misreading, because I'm just seeing "if the derivative of X is zero, then doesn't that automatically mean X must be zero?"

I'm supposed to find the $z$-component of magnetization of a sample of $10^{23}$ atoms in a given p-state. If I find the expectation of $\mu_z = L_zQm_e/2$, could I divide by some arbitrary $dV$ to get $m$?

Yo I have a really dumb question to settle a really dumb conversation

Say that you have a door you want to pass through, and it's been closed but that event hasn't reached you yet, and you can run along a spacelike path, can you pass through the door?

@Phase I know next to nothing about the topic; but unless you could travel in the spacelike path faster than light, I don't think it would matter

well spacelike would entail faster than light anyway

It's probably gonna end up being that the question contradicts itself or I'm dumb af but I figured I'd ask

Sup humans!

A quick question. What maths will be considered "complicated". I mean, I want to learn something out of my comfort zone and complicated math certainly does the job. Is calculus considered enough complicated for a 16 year old?

In the UK, age 16 is the usual age at which children start learning calculus in school

@NovaliumCompany Pieces of knowledge don't come with age labels. It's not like how movies are PG-13 or something.

depends what you mean by Calculus

@NovaliumCompany What is the ultimate goal? For example, I enjoy studying maths because it helps give me the skills with which to further my study of physics

But if I can give any advice its not to learn things in a poor order

Get the prereqs up to snuff

I just want to exercise my brain and maths seem like a nice way to do so.

I already read books and learn layman of different fields.

why not start with something that is "complicated" but "basic"

@NovaliumCompany Are you in full-time education that will eventually cover calculus?

like one of the fundamentals

Why not learn some analysis

@BetaDecay Nope, I live in Bulgaria and I don't think we're learning calculus in the near future.

the basic parts

Anyways I have some idea of it.

that dont require any calc i mean

actually my idea is probably bad

Maths seems to introduce the brain to different topics and different ways of viewing things and dealing with problems. What else interesting is there to learn except calculus?

Matrices maybe?

yeah

i was gonna suggest linear algebra

@BetaDecay I was thinking exactly this.

It will give you a better intuition for a lot of physics stuff you'll learn too

@Blue I've never said there isn't anything else. I'm just asking what else there is. (a specific answer)

I was thinking QM without maths but... I think it'll be a mistake ;\

I have no idea how I'd have liked Circular motion if I hadn't gotten familiar with basic linear algebra

QM kind of is maths

i mean its not but

When you do it it might as well be maths with a lot of initial conditions and empirical cheats

Wave functions of stuff and other electrons sweeping through slits seems interesting.

If you want to do QM, do linear algebra

You'll need it

Unexplainable stuff going around in this harsh reality.

Particle duality...

Entanglement

I have some idea of the concepts but no idea the maths.

oof

I dont trust anyone who makes statements about QM in words haha

@Phase Already did quite a lot of it. But I'm sure I'll still learn some stuff along the way.

@NovaliumCompany you have?

My QM lectures atm are just solving the schrodinger equation. No introduction of linear algebra whatsoever

Ew

Matrix mechanics masterrace

@Phase Yep. Not too advanced, but if I don't understand something, I google, and that way I really memorize it, because I know where it can be applied.

That sounds like how I started learning things

@BetaDecay Holy Avengers Endgame, u a professor?

do yourself a favour and get / download a textbook

Structureless googling wont get you far

@NovaliumCompany First year undergrad. But close enough ;)

@Phase It actually got me quite for in some fields.

Don't trust that

It's easy to think you have a better understanding than you do if you only read and never test or apply

@BetaDecay I've always wanted to meet a professor in real life, u seem pretty cool.

I bet you're like Dumbledore.

@BetaDecay wait how did they start?

@Phase I agree reading is a perfect way to aquire knowledge, but you don't learn swimming by reading a book.

They started RIGHT at solving for a well? and havent done anything about bra-ket etc?

@Phase Nah, nothing bra-ket

I'll get a pic of the syllabus

@NovaliumCompany you learn quantum mechanics by reading a book

I'm not sure what your point is

@Phase Agree 100%.

@Phase Me neither :D

Fair but please heed my warnings D:

You will end up uprooting your study and doing it again from the start if you don't have it so that you learn each thing in it's right place

I mean, I learned to program many computer languages by just googling stuff... I never read a book on programming and my skills are quite advanced.

I recommend Shankar's Principles of Quantum Mechanics once you've gotten Lin Alg to a good standard

We did the Bohr model, then used energy to derive the Schrodinger equation

I'm currently rereading this for the third time amazon.com/Zero-One-Notes-Startups-Future/dp/0804139296. Pretty intersting stuff.

what a meme

@JohnRennie Hi John, thanks for taking the time! I appreciate it. between the three of your guys' answers, my confusion has been cleared. I added a closure to the bottom of the post to put the nail in the coffin. cheers

Douglas E. Richards is god...

If I just had the chance to meet this human being.

uh

he seems like a sci fi author to me

x)

I already read 3 of his books. Dude.... just...

There are some deep thoughts and ideas hidden there.

Isn't it sci fi..?

Yep, but some of the ideas can become sci.

Touchscreen phones and wireless communication would have been considered sci-fi a century ago.

Well yeah but that's more just a case of him having a good guess at what Engineers would make later on

I don't care... I just enjoy the books and I would love to have a sci-fi conversation with him some day.

@NovaliumCompany You might enjoy Asimov

Or even Kepler

I enjoy simple books with deep thoughts about reality and stuff...

@Blue Pretty boring still... I'm ahead in Biology, Physics, IT...

@Blue 10th :)

@Blue Time flies.

@Blue I can't wait to see what you'll do after university.

@Blue 10th grade math seems all about sin, cos and some formulas including those.

important stuff!

@Blue Nope...

Noval have you learned $$\sin ^2(x) + \cos ^2(x) = 1$$ yet?

They just make us memorize random formulas without explaining anything about them and just expect us to put them in the test. It's all about, just use the formulas put numbers in and think less...

@Phase We're quite ahead of that already. (That was last year)

oh ok I just thought it was cool because it's vectors

Lol our math textbook for 10th grade costs 4$ xD

I've heard rote memorisation is a big thing in India and China

It doesn't matter what you do, there's always and asian better than you :D

Indians are pretty smart as well ;)

Are russians smart?

Welp, Bulgarians are quite average. Not many smarties around here in Varna.

god that reminds me of some dude I argued with

said that even farmers in india knew calculus

i said "india stinky" as a joke when someone posted one of the river pics

and he raged at me for a good while then wanted me banned from the dc server

I discourage the replacement of regular real-world social communication with this chat room. (I'm just saying this, because it's like being really hungry and opening a picture of a burger on the computer screen and expecting to get fed up)

yeah dw

I come here like once a year

7cups.com That's a really interesting thing I discovered a few days ago.

This better not be goatse

oh

Hahaha

uhh, you ok Nova?

@Phase Haha I am, don't worry. Everyone has worries and stuff... but It's important to work on them. I just "woke up" 6 months ago. I decided to get out of my comfort zone, start attacking fear, stop being a pussy and do things like a man.

fair enough ig

I had no friends, I lacked social skills... long story short - I was "the nice guy".

Complete scared to talk to anybody.

I'm no one to judge but I guess those who spend regular time here or any other "social simulation" don't have many friends in real life and are social "weirdos".

I'm just saying this because I used to be one.

uhhh

That's a very strong statement

Alright. Good night everybody. I'll go now. It was nice catching up with you.

goodnight sleep well

@Blue stop lying i've read your diary

^ ;\

@Blue is 0celo7 still b&

@Blue Don't take this personally. I'm just giving you some advice. Take it if you think it's right. But believe me, I went though a radical life change, and it's AWESOME!

We're happy for you but different strokes for different folks my dude

@Blue Of course. I'm not trying to prove anything, please don't take this personally, I'm just getting my thoughts out, because I used to be in a similar position to yours, and many many many people still are. Computers replace regular social communication and people begin to stay in their comfort zones, and that's bad.

@Blue As long as you continue with that mind set, you will never achieve what you want to achieve. You cannot continue to hide behind the computer screen. Some day you'll need to talk to real people, some of them will be assholes, you won't know how to take it...

through with my quantum qual, good feeling :D

@Blue Exactly! I don't know you in real life, so I have no idea who you really are and I can't give you any advice. I'm just laying my thoughts out nothing more. If you have anything else to ask please do, otherwise I'll hop under the sheets.

Long story short, when you've decided you want to change, you will, that's it. :)

@Blue :)

How can I calculate K of this reaction? HF +OH- <---> F- + H2O?

really, really happy I remembered $[\vec{S}_b \cdot\vec{S}_a,\vec{S}\cdot\vec{S}_c] = i\hbar \vec{S}_c \cdot (\vec{S}_a x \vec{S}_b})$, didn't think that would ever come in handy...

sorry, this:

$[\vec{S}_b \cdot \vec{S}_a,\vec{S}_a\cdot\vec{S}_c] = i \hbar \vec{S}_c \cdot (\vec{S}_a \times \vec{S}_b)$

Any ideas?

@Curio long time since I've done chemical kinetics. this looks like a decent resource: chemistry.bd.psu.edu/jircitano/kinetics.html

if that's even what you're asking XD

@EmilioPisanty I solved the problem.

It's quite interesting.

@dm__ Yeah it is, but it doesn't talk about my kind of problem

@NovaliumCompany that's... kind of out of line, to be honest.

(just saying)

I imagine it's too much trouble to write down the details

@DanielSank nice :)

@DanielSank nice :)

@BetaDecay looks like my adventures with tensors

@EmilioPisanty hahaha, oops.

No wait... did I tell you I solved it twice? I'm confused.