And you'll note that that has $S=kx-\omega t$, so $J/\rho = \frac{1}{m}\frac{\partial S}{\partial x}=\frac{k}{m}$

okay, $\omega^2$?

??

never mind :P

And since $\rho=\sqrt{R}=1$ in that case, you'll have $J=k/m$ i.e. a constant probability current

(I was thinking in oscillations)

The reason is actually rather natural: In a scattering experiment, you're typically sending in a bunch of particles rather than just one

Hence why you can describe it as a plane wave rather than a wave packet

ah okay

I'm roasted:P

So it shouldn't be surprising that you have to keep 'injecting' probability density, i.e. events, into the system. if you stop shooting particles in, you'll stop getting transmission and reflection

that makes sense

Bottom line is that, when you do bound states, you can assume $J=0$ at infinity without any issue.

But when you do scattering, you definitely -can't-.

(Scattering is a bit weird like that. Physicists definitely play fast-and-loose with the justifications for those problems.)

haha, right, that's easy to remember

it's intuitive, in a way

The rules don't entirely go out the window, though.

When you do scattering, you'll find that $J_{in}=J_{reflected}+J_{transmitted}$.

There's still an version of conservation of probability. But it's in terms of the relative fluxes: Each particle I send in is either transmitted or reflected, and the probabilities of those two events will add to 1.

right.. sorry that I can't really ask anything substantial anymore:P I'm justing taking what you say as "truth" at this point

lol

One weird thing this leads to is that you don't 'normalize' wavefunctions in scattering problems like you would in bound state problems.

It's a lot more arbitrary.

(Which actually can come in handy for problem-solving if you're clever, but that takes practice and experience.)

yea, well that's far ahead of me. I have to understand stationary states first:P

lol

You definitely will run into scattering states, though. No way you'll miss that.

It doesn't show up until chapter 2, though.

well chapter 1 nothing, chapter 2 is huge

lol, the last chapter is apparently called "Scattering"

gotta eat something now tho!

well, the scattering stuff in chapter 2 is in section 2.5

but that's scattering in 1D. scattering in 3D is the last chapter and is haaard

ah yea I see

:'(

It's pretty brutal.

TEDDDDDDD

Where are you!?

hello math people!

@TedShifrin a man here is looking for you

@TedShifrin So, I got the call today from Queens. He sort of stumbled around his words and lied and said that it had to do with documents coming in after the deadline (they reviewed my high school that came in on the 10th but not my ILC that came in on the third.) He then recommended I pay another 160 dollars to apply to do part time studies, which would also set me back half a year. Another strange thing is that my phone did not ring. Instead it just popped up saying I had a voicemail.

wait for 20 minutes more!

he will be there I think from my statistic thinkng!

:)

@TedShifrin I called back and told him that I know for a fact that they didn't see my ILC on my application and then only looked at my highschool and that there was no way I was going to pay another 100 dollars. Of course, all calls go straight to voicemail so I had to leave a message. I am now contacting his boss to see what she can do.

Hey everyone!

Hey manny vaughn

Hi

BALARKA!

yo

How's it going you rebel.

still working on revolution

@BalarkaSen got any more books? ;-)

That's revolting.

@Daminark Hey~

only as long as you use a revolver

@BalarkaSen Hey

How's it going everyone?

i'll just give everyone the plague. Then we will all be very revolting.

so you say you want a revolution, oh well, you know

@BalarkaSen i meant mathematical books

but revolting is so much woork

:P

balarka is banned again

No way.

i'm sure the one person flagging him repeatedly feels great pride

He better not be banned again.

i hope not

that'd suck

You're joking, right?

This frivolous flagging epidemic needs to stop

Who could possibly be flagging him.

We are all friends!

You can ban people here?

Did you guys watch my youtube video, I've never seen the movie but it's pretty hilarious I might have to watch it.

Am surprised am still here...

I'll just say this guys, if you keep flagging Balarka and he keeps getting banned, he won't come back.

@demonark well then knock it off.

And we'll lose one of the best mathematical talents, and most wonderful people I've ever had the opportunity of meeting.

Somehow the person who keeps doing it is likely not to be disappointed

@Duck riight... yeah sure

well you are a demon

I'm a demon with morals!

That's literally just an angel

but demonic morals are things like hatred and greediness

We should all post in the meta and let the mods know that the flagging is getting out of hand!

sounds good to me

who wants to write the question?

I think dodsy is the one doing the flagging

that would make sense

he's new here

what would be ironic and kind of funny is if balarka has been flagging themselves, deleting the comment, and then going away for an hour just to prank us.

balarka come here

mse4me.chatovod.com

Yo chat

Wassup my man

Hey @Astyx

How are you all ?

Doing alright, how about you?

I suppose daminark now speak for us all

Yup

I'm good thanks

That's cool with me :p

I finished my peaceful run by the way

It has been decided that everyone is doing alright! :D

Ah, how'd you like the Asriel revelation?

if you guys want to talk to balarka we are over here: mse4me.chatovod.com

Like, the plottwist ?

It made sense and was pretty good

Removed

Can someone help me with this small problem?How do I simplify 2^{ln3/ln2} to get the answer=3?

Duck that was a dirty trick.

@Tatan $a^{x} = e^{x\ln(a)}$

@Dodsy what was?

@Dodsy did balarka say I banned them or something? I didn't think he was back yet.

hi

@DanielFischer Hi, so there has been multiple totally ridiculous flags going on in here for some days. I was the target of one yesterday and got banned on a particularly harmless joke but I shrugged it off as amusing. Today I got flagged and banned for a really non-offensive comment. So I thought I'd report it to you.

Hello @Abhishekstudent

I would appreciate it if you'd investigate the flag logs.

Guys, they always say that a differential equation is an equation involving a function and its derivatives - but shouldn't we say that it involves a functions and its derivatives, and possibly the independent variable?

is $x^3$ a polynomial

Yo @Sha, @Balarka

Hey

hi @Astyx

or does it need to have all the powers

@Abhis yea that's a polynomial

Ya it's a poly

@BalarkaSen good idea

thanks

@Sha Not really, the independant variable does not have much meaning, it's an equation of functions

oh I think I know why I got confused

Balarka is back!

I saw this

hm actually

That's equivalent to $F(y, y') = 0$ in some sense

yay!

@BalarkaSen what's up man?

oh, how then? @Astyx

Well you can equivalently write $y(x)f(x) + y'(x) g(x) = h(x)$ and $yf+y'g=h$

@BalarkaSen Well, that sucks.

I think it's just hate-flagging by someone dumb

perhaps

Me too.

@Balarka can't moderators see who did it?

Yeah I think they can

They can.

That's why I pinged a moderator.

can someone just flag and ban you though? I thought flags had to have some merit behind them or they get refused...?

(unless 5 people are simultaneously flagging, which then indicates an actual problem)

hm not sure if I understand where this $f,g,h$ comes from @Astyx

Just 10k users approve them

There is 2 balarka

so we're looking for a 10K user with a grudge.

I think the one without sen is a spy

@Sha These are just other functions

oh

@Zee what are you talking about?

so the functions don't matter in solving for $y$?

The mods will sort it out, perhaps stop speculating for now ?

yeah

@Sha Of course they do ! They define the differential equation

Yeah better to just leave it now. I'm going through the worst shit over here boys and girls.

Roger that

ugh, I hate this. haven't had it properly at school, but I'm still supposed to solve them. I guess I should just try more examples first @Astyx

@Dodsy what's wrong?

Shitty admissions practices that aren't getting me anywhere and I'm being shafted.

O.O

@Sha You should get used to them yeah

@ShaVuklia Start with easy things. Constant coefficients, for example.

First order differential equations with constant coefficients are not that interresting :p

Of course not. But it doesn't hurt to start at the bottom and move up at your own pace.

@TheGreatDuck Whereabouts in the states are you from, Duck.

colorado

why?

Of course @Steamy

Oh just wondering.

I should be doing math right now...

ookay

@Dodsy how'd you know I was in the states?

I read so earlier when you were speaking of the trump administration.

wait actually

maybe I'm just too lazy

I'll try to solve it my own

@SteamyRoot excellent advice :-)

@Dodsy oh. fair enough.

oh okay, it was not that hard. didn't see it first

@SteamyRoot Like with piano, everyone wants to play a Chopin piece, but you have to learn row your boat first.

I thought you said 'to row your boat' at first

Lol so did I

It didn't even shock me

Learn to row boats before doing a piano, kids.

kids?

Hi chat

Yo Alessandro

Yo

yo

are you happy?

about?

math of course?

sorta, are you?

i am happier with physics.

Hello

Hi

i am happier with biology

;)

how so?

I was quite happy with biology when in high school.

So this is just a casual chat?

yup

@Espinoza We talk about math and about posts on here

But mostly share cool math things

talk about homework

but I am happier with physics than biology when university because biology in university includes overwhelming professional terms.

@Espinoza Sometimes we actually talk about maths

That's great.

Yeah it's pretty casual

and Ted Shifrin comes here all the time.

Sanity check: an entire function has a power series at any point with infinite radius of convergence, right?

how do we chat about math here? can math symbols by typed here?

I have a cool question if anyone's interrested : Let $G$ be a finite group. Prove that the probability of two randomly chosen elements commute is $1$ or less than $5/8$

@Captain See Latex inchat url on the chat description

In the top right

@AlessandroCodenotti Yes. The radius of convergence of a meromorphic function is the largest disc you can draw until you hit a pole.

@CaptainBohemian math.ucla.edu/~robjohn/math/mathjax.html

@MikeMiller thought so, thanks for confirming

@BalarkaSen That sucks. Unfortunately, as far as I know there's no way for me to find out a) who raised and b) who validated those flags, so no idea whom I should have a word with.

Hi @DanielF @Alessandro @Astyx @Balarka @Dodsy

I think it's more or less community knowledge who was raising the flags, @DanielFischer, but of course that's not actionable. I think the implicit general question here is "If I continue to be flagged and banned for things I consider harmless, and I think this is done to inflict harm, is there somoeone I can/should talk to about this?"

Yo @Ted