The h Bar

dm__

03:15

generating a rank $k$ spherical tensor out of two spherical tensors, of rank $k_1$ and $k_2$, is analogous to adding two particles with total angular momenta $k_1$ and $k_2$. insane.

Avnish Kabaj

Where's that article which says that mods are supposed to be the most active members of the community

dm__

03:47

$J_{\pm 1} = \mp J_{\pm}/\sqrt{2}$. this is perverse.

if anyone can make sense out of the projection theorem, please share.

user8718165

05:43

Good morning sir @JohnRennie

John Rennie

06:01

@user8718165 morning :-)

user8718165

:-))))

@JohnRennie, I had a doubt, are you free now?

John Rennie

@user8718165 yes

user8718165

:-))))

Lets say I have a very strong sealed vessel (pressure cooker) in which I'm boiling water. I raised the water temp to 120 degrees. Now I somehow open the lid will all water vaporize?

John Rennie

The way you do this is to first calculate the energy needed to vaporise all the water. This is simply the mass of the water times the latent heat of vaporisation. OK so far?

user8718165

06:19

yes sir

John Rennie

@user8718165 as water evaporates it cools the water that is left i.e. the heat needed to vaporise the water comes from the heat in the liquid water. And if the water cools below 100°C it will stop boiling.

So the next step is to calculate how much heat is released when the water cools from 120°C to 100°C. This is just the specific heat times the mass times the temperature difference of 20°C. OK so far?

user8718165

yes again sir

Now if that energy = the latent heat required to boil all the water, then will the water boil?

John Rennie

Yes.

user8718165

@JohnRennie does that mean if I sufficiently heat the water in a pressure cooker such that all the water molecules have sufficient latent heat to vaporize then there will be no water left in my cooker?

John Rennie

@user8718165 Yes, and you can easily calculate how hot the water would have to be.

user8718165

06:32

yes sir and it depends on the amount of water right?

John Rennie

@user8718165 no, it doesn't.

That's because the mass of water you are evaporating is the same as the mass of water in the pan.

user8718165

more water will require more latent heat so more heating will be reqd.??

John Rennie

Suppose you double the amount of water, then you double the energy needed to vaporise it. But you also double the amount of energy available from cooling the water from 120°C to 100°C.

The two cancel out, so the energy needed to vaporise all the water remains the same.

user8718165

@JohnRennie how will the water evaporate inside the pressure cooker?

John Rennie

@user8718165 the water won't evaporate if you keep the pressure cooker closed, but your original question asked about the evaporation if you took the lid off.

user8718165

06:40

will both evaporation and boiling happen at the same time?

after opening the lid?

John Rennie

06:54

@user8718165 the word boiling is a bit vaguely defined. It can refer to the water turning to steam, but also to the bubbling you get when you heat water to its boiling point. I'm using the terms interchangeably i.e. the water is turning to steam and I'm not too concerned about whether we call that process boiling or evaporation.

user8718165

do you mean boiling is a type of evaporation?

John Rennie

In both processes liquid water converts to water vapour.

user8718165

I mean evaporation at the boiling point?

user8718165

07:09

@JohnRennie I couldn't get it fully, Lets suppose I took 18g(1mole) of water in the pressure cooker and I heat it to 100 degrees and then continue to heat it and add 9720 cal of energy to water which is sufficient for the water to vaporize. Suddenly i remove the lid. What will hapeen ?

John Rennie

All the water will instantly turn into steam

user8718165

@JohnRennie can you please explain this to me. I couldn't get it

John Rennie

@user8718165 You mean about doubling the amount of water?

user8718165

yes sir, if I do that then what will happen?

John Rennie

You've already worked out that if you take 1 mole (18g) of water you need to add 9720 cal to get it hot enough to boil instantly. Yes?

user8718165

07:16

yes sir

John Rennie

@user8718165 The molar specific heat of water is 18 cal, so the temperature increase of the water would be 9720/18 = 540°C. So the temperature of the water needed for instant boiling would be 100 + 540 = 640°C. OK so far?

user8718165

yes sir

John Rennie

@user8718165 OK, so now take double the amount of water i.e. two moles. Now you need 2 x 9720 = 19440 to vaporise all the water. Yes?

user8718165

yews irr

yes sir

John Rennie

The specific heat of two moles of water is 2 x 18 = 36 cal/degree. Yes?

user8718165

07:24

ok sir yes

John Rennie

So the temperature increase of the water is 19440/36 = 540°C.

user8718165

yes sir

so the proportion remains constant?

John Rennie

Yes. Suppose you have n moles of water, then the energy required to boil it is 9720n.

And the specific heat is 18n, to the temperature increase is 9720n/18n = 9720/18.

The number of moles n cancels out, so the temperature increase doesn't depend on how much water you have.

user8718165

ok sir I get it now. Could you please tell me what do you mean by this thing "But you also double the amount of energy available from cooling the water from 120°C to 100°C"

John Rennie

@user8718165 if you have n moles of water then the energy available from cooling the water from 120 to 100°C is E = n x 20 x 18 cal.

So if you double the amount of water, i.e. double n, then you double the energy E.

user8718165

07:37

Sir do mean that with every energetic water molecule vaporizing with the latent heat, the bulk of the water cools a bit?

do you mean that****typo

John Rennie

@user8718165 Yes. The energy required to eject a molecule of water as vapour comes from the thermal energy of the liquid water. So as molecules are ejected the liquid water cools a bit.

@user8718165 you can edit posts after you've clicked Send.

user8718165

wow!! how to do that?

John Rennie

Are you using a phone or a laptop?

user8718165

desktop computer...

John Rennie

user8718165

07:41

click on edit??

John Rennie

Click on the triangle to the left of your post and choose "Edit"

user8718165

Thank you sir

I wanted to know one last thing

John Rennie

Yes?

user8718165

If I heat 2 moles of water to 100+(540/2)=270+100=370 degrees then instantly after opening the cooker lid, I'll be left with 1 mole of water. right??

John Rennie

Yes

user8718165

07:51

Ok sir. What will happen if I open the lid when the water temp. reaches 100 degree?

all the molecules are at 100 degree.

John Rennie

We assume that the steam and the water are well mixed so they cool together i.e. after the system has settled down both the steam and the water are at 100°C.

user8718165

@JohnRennie didn't understand this

John Rennie

Imagine the change happening a bit at a time. The water starts off at 370°C so the first few bits of steam produced will be at 370°C. But we assume that the steam and water stay mixed (as a kind of mist I guess) so as the water cools it cools the steam around it as well.

So both the water and the steam end up at 100°C

user8718165

ok sir got it

now will the remaining water stop boiling after reaching 100 degrees?

John Rennie

Yes, because ejecting any more water molecules will cool the water to below 100°C, and obviously below 100°C it doesn't boil.

Loong

07:59

@user8718165 I think we have a question like that on Chemistry: This or this

undefined

08:11

@EmilioPisanty regarding your chat reply to me from yesterday about the term "expat". I would like to say that at least in my Country (Germany) the term "expat" is associated with something nice and valuable, while the term "migrant" is very often used in racist and discriminating ways. Personally, I have never heard of a racist/bad use of the term "expat"

user8718165

@JohnRennie when all the water molecules are heated to 370 degrees, some of the molecules leave the water as steam but other molecules in the bulk of the water still have that 370 degrees then how does the liquid cool? I'm not getting this.

Slereah

morning

John Rennie

@user8718165 it takes energy to eject a molecule of water as steam, and that energy has to come from somewhere. It comes from the thermal energy of the remaining water molecules. So the bulk of the water does not remain at 370°C. It cools to very slightly below 370°C.

user8718165

ok but the water molecule which is leaving also has (100+270)degrees

John Rennie

@user8718165 so we get a small amount of steam at 370°C and the bulk of the water is very slightly cooler than 370°C.

We're assuming that the steam stays close to the water long enough for the water to cool the steam to be the same temperature as the water i.e. also slightly less than 370°C.

user8718165

08:26

so that extra energy is there with the molecule as it leaves and still it takes a bit more energy from the bulk to vaporize and this process continues...???

John Rennie

Yes.

Emilio Pisanty

@undefined that's completely missing the point.

user8718165

@JohnRennie let the steam be at 370 deg and the water at 369 deg. after sufficient time the bulk water and the steam will both be cooled to 69.5deg right??? I think like this

This process continues and the water cools further

Emilio Pisanty

First of all, the fact that you in particular do not use the term in a problematic way does not mean that there are no situations where it is, and if you're going to use it as a banner then it behooves you to understand those cases

user351417

This is ridiculous. I've been reading all those jokeß and wondering what the hell's going on because I've been reading it as 'beta' in my head all along :(

John Rennie

08:35

@Chair It's all very confußing

4

Emilio Pisanty

@undefined But secondly, you very much sound like you're in the problem area. Can you provide a clear and unambiguous definition of both terms, and the difference between them?

> the term "expat" is associated with something nice and valuable, while the term "migrant" is very often used in racist and discriminating ways

John Rennie

@user8718165 it's not usually helpful to try and explain processes like these at the detailed molecular level because in real life the process would be messy. When you open the pressure cooker you'll get a huge explosion and there will be a big cloud of stea,m that is probably at different temperatures in different parts of the cloud.

Emilio Pisanty

what is it that a migrant needs to do to be accepted into the club of "nice and valuable" migrants? Be white? Not be poor?

John Rennie

@user8718165 We're using a rather idealised approximation where both the water and the steam end up in equilibrium at 100°C. And our calculation of the temperature is based on this approximation. In real life our approximation would be wrong for lots of reasons.

Emilio Pisanty

Would you use the term "expat" for someone from Turkey, or Angola, or Lebanon, or Vietnam? If not, why not?

Slereah

08:41

I always thought the distinction was more that an expat was not a permanent resident

user351417

@EmilioPisanty At least in India, the biggest difference I can think of is the reason for migration. I think we sometimes use the word migrant when talking about people from other parts of the country (typically rural, though I'm given to understand that the US/Europe definition of rural is extremely different from Indian city-peoples'), but only for blue-collar jobs. For people who migrate but are in white-collar jobs, we don't use any word which implies 'from outside'.

Emilio Pisanty

Say, an entrepreneur that owns their own business, or someone who works in such a small company

user8718165

@JohnRennie ok sir so ideally can we say that the hot steam cools itself a bit by passing a little energy to the bulk water so that both the steam and the water are now below 370 deg?

John Rennie

@user8718165 yes

user8718165

@JohnRennie thank you very much sir...:-)))

got it now

Emilio Pisanty

08:44

@Slereah sorry, Sam, I'm on the move. But I did want to drop off this questions for @undefined, given at s/he stepped in to defend the term.

user351417

I figured I'd mention whatever I just did because I had to bounce rather abruptly yesterday.

undefined

@EmilioPisanty good morning. Well, I guess I mussed your point because I cant see something negative in the term "expat". It wasn't my intention to offend you or anything and I apologize if I did.
for me the definition of the term "expat" is someone who moves to another country to work and live there, mostly people with higher education and "good jobs" (having the intention to move back or not doesn't matter).
and the definition of the term "migrant" for me is something like someone who move to another country because he/she expect a better life quality, welfare, and just a better life than…

@EmilioPisanty I feel like this discussion is on the edge to racism. And therefore I'm not sure if I should answer this question

Emilio Pisanty

09:38

@undefined as discussed above, that's more of a classist stance than a racist one, though the distinction is pretty moot given the strong correlations between the two. But in any case, saying "oh, no, our site name is not racist, it's exclusively classist" is hardly a defense.

@undefined As I already argued, the term as used in Germany serves a clear racist function. If you don't want to contest the argumentation, then you're effectively conceding the claim.

I perfectly understand that this can be deeply uncomfortable - taking account of one's privilege always is. But saying "I don't want to talk about it" doesn't make the problems go away.

undefined

@EmilioPisanty @EmilioPisanty no no, I would like to talk about. But some people are easily offended by a discussion like this.

@EmilioPisanty expat and migrant is very distinct for me. (I think, I can always only speak for me and about my views.) For example I would like to be an expat in Argentina but I would not like to be a migrant there.

@EmilioPisanty well, I can only repeat myself. For me the term "migrant" is known to be often used in a racism way, not the term "expat". But maybe I also think so, because I feel that nowadays people (I don't mean anyone specific) are often offended by words which were used for many (hundreds) years. and all of a sudden, they make a big fuss about it. And this is an attitude I dont agree with. I mean this more general and not (only) in relation to expat/migrant

As I said, I feel like this is an extremely subjective topic. Possibly influenced by personal experience. Nothing suits me further than to convince anyone that I am right or that only one side is the right one. Rather, I think that there is more than one right.

And to be honest, I would prefer to talk with you about physics than about this :)

Emilio Pisanty

10:16

> For me the term "migrant" is known to be often used in a racism way

that's dead wrong

there's nothing intrinsically racist about the term "migrant"

as the OED defines it:

> migrant, n. A person who moves temporarily or seasonally from place to place

any additional baggage added to the term is local to the culture and says more about the culture than about the term

> For example I would like to be an expat in Argentina but I would not like to be a migrant there

so basically what you are saying is "I would like to migrate but I would not like to be discriminated against"?

I'm not sure where you see a distinction to any other migrants. Do you think the people you refer to as "migrants" want to be discriminated against?

undefined

@EmilioPisanty no, I would like to go there for a good job (and therefor in my understanding being an expat)

Emilio Pisanty

@undefined So there is no distinction between 'migrant' and 'expat' other than the purely socioeconomic distinctions you described above, then

undefined

@EmilioPisanty alright, then I have to admit that I'm influenced by my culture

Emilio Pisanty

@undefined then when your culture does racist or classist things, own up to them, or change your usage.

undefined

@EmilioPisanty socioeconomic distinctions and (but not always) cultural background, like the country/culture they are coming from.

Emilio Pisanty

10:24

@undefined so basically you're agreeing with my initial comment

undefined

@EmilioPisanty the term "expat" is rarely used in Germany anyway. But I think we have a german word for it. But which is different from the term migrant

Emilio Pisanty

@undefined what's this german word?

> the term "expat" is rarely used in Germany anyway

by Germans, perhaps. But there are significant migrant populations in Germany (primarily in major urban centers, primarily from European and North American backgrounds, mostly English-speaking, generally quite affluent) that very much use the term to describe themselves.

undefined

@EmilioPisanty Auswanderer

Emilio Pisanty

@undefined That is very different. Do not confuse 'Auswanderer' and 'expat' for synonyms.

undefined

@EmilioPisanty yes and those are not expats but migrants

Emilio Pisanty

10:28

@undefined ... by which you mean ... ?

undefined

@EmilioPisanty that would be the closest German word I can think of. Or do you know a better one?

Emilio Pisanty

@undefined I don't, but there is no requirement that every word in language A have an exact equivalent in language B

it is a mistake to think so, and it is a mistake to look for such equivalents

undefined

@EmilioPisanty that would lead us to the huge topic of Germany immigration politics. And I'm not sure if we really wanna go down this road

Emilio Pisanty

I would be extremely surprised if there was an exact equivalent to the word 'expat' in German. Given your passionate defense of the term in English, are you really sure you fully understand it and its connotations?

still, all of that is pretty moot

7 mins ago, by undefined

@EmilioPisanty socioeconomic distinctions and (but not always) cultural background, like the country/culture they are coming from.

basically you're agreeing with this

21 hours ago, by Emilio Pisanty

they should rename it to the correct version, "Immigrants (but only white and affluent ones) Stack Exchange"

undefined

@EmilioPisanty true but I think if a word doesnt have an equivalent then the meaning of it is influenced by the local culture

Emilio Pisanty

10:32

perhaps with less emphasis on the whiteness

@undefined try finding an English equivalent for "doch"

undefined

haha I so often tried and failed (because there is none) that I teach my Argentinian friend the meaning and use of doch

Emilio Pisanty

so why would you expect there to be one for 'Auswanderer'?

undefined

well, the dictionary (EN-De) list: expat - im Ausland Lebender / im Ausland arbeitende Person (living in a foreign country / in a foreign country working person)

so we have an explanation more than an exact equivalent word

Emilio Pisanty

I don't want to get bogged down in details, I don't have that much time to spend.

undefined

if we translate (De - EN) Auswanderer, it translate to Expat

@EmilioPisanty yes, I think we should settle this too

Emilio Pisanty

10:40

and you've yet to produce any meaningful arguments to refute any of the core points I laid out earlier and yesterday

undefined

I dont want to refute anything you said

who I am to do that?

Emilio Pisanty

@undefined so you agree that the term 'expat' often has a racist and classist structural function, then

undefined

@EmilioPisanty I agree that the term expat maybe often has a racist and classist structural function in its usage outside of Germany, even tho I've never heard about a "bad use" of this term

user8718165

@JohnRennie hello sir

Emilio Pisanty

@undefined and you're still OK with having a word with this baggage attached to it as the masthead for an SE community you're part of

undefined

10:51

@EmilioPisanty I feel like I'm not qualified to answer this because I have no negative associations with this term because I never experienced anything negative with this term. But taking into account that this is not a new SE community and therefor this term is used for quite a while now and that I dont like changes like this in general, I would say that I am okay with the name of this SE community. Because if we start there, where would we end?

John Rennie

@user8718165 I'm busy I'm afraid ...

user8718165

no problem sir...thats fine

undefined

For one this term is offending, for the next the other term is, the next person want to add gernderless terms everywhere and so on and on. In my country they even argued about renaming and deleting word out of a classical children book because "it could be offending". And thats the point where I ask, if those people are really serious. I dont like that

Emilio Pisanty

@undefined that's a pretty remarkable comment - basically "We've been using classist language for a long time now, so why should we stop?". If you're OK with that kind of attitude then I'm not sure there's anything more I can say.

undefined

can you explain the word "classist" in this context?

Emilio Pisanty

10:54

> Of, relating to, or characterized by classism; discriminating on the grounds of social class.

(as the OED puts it)

if you want the OED's take on 'classism', that's

> The belief that people can be distinguished or characterized, esp. as inferior, on the basis of their social class; discrimination or prejudice against people belonging to a particular social class.

anyways, I'm off for lunch.

undefined

thank you. Well, I mean I get discriminated by my social class every time I visit a doctor and there comes one who has more money than I have. I wont say its good but its how the world is working

have a good lunch

user8718165

@JohnRennie whenever you're free please tell me whether I'm correct or not. I'm thinking like: I'm boiling 36g(2 mols) of water in a pressure cooker and begin to heat it...eventually the water reaches 100+(540/2) degrees, I open the lid, theoretically, 1 mol will instantly vaporize leaving me with 1 mol water at 100degrees. But practically I'll be left with a little more(than 1mol) water as the steam will cool down my water by a bit every time a molecule vaporizes.

@JohnRennie Since every time a molecule vaporizes, molecules in the bulk collide with the vaporizing particle and lose a bit of their momentum. This way the bulk liquid cools as water molecules vaporize. Am I correct sir?

user8718165

11:32

@JohnRennie hello sir are you free now?

Zerix

12:00

Why does susceptibility decrease with increase in temperature?

user8718165

@JohnRennie Sir please tell me just once whether my way of thing is wrong or not when you are done helping in the problem solving strategies. That's the last thing I'd like to know.

undefined

12:36

@EmilioPisanty just for your information: I was curious and ask on a German student platform if anyone ever experienced something negative with the term "expat". I know its not representative but a fair amount of people answered that they never heard of anything negative. And most associate with the term "expat" someone who was sent abroad by his company to work there

PM 2Ring

The OP has clarified his on-hold question. Is the policy to re-open & dupe close, or just leave it? There are half a dozen possible dupe targets in the comments.

Emilio Pisanty

@undefined You seem to have completely missed the point.

Heck, you seem to be missing the forest for the trees.

It's the very fact that people don't find it 'negative' that's the core of the problem. It's a structural (social and cultural) means of whitewashing some types of immigration. Of course the whitewash looks clean.

undefined

@EmilioPisanty I dont think so. But to be honest I dont see how I could have missed your point. If only a minority associate something negative with a term, why should it be changed if most people even think of something positive when they hear this term?
Where is the problem if most people dont find it negative? Seems you're right that I really dont fully get your point

PM 2Ring

@undefined Emilio isn't saying that "expat" has negative connotations. If there was no discrimination, we'd just have a single word for migrants. But because there is discrimination, we have two terms that create a dipole: "migrant" means undesirable migrant, and "expat" means desirable migrant. And so by using this polarising terminology of "expat vs migrant" we maintain the attitude of discrimination.

Emilio Pisanty

↑ that, in a nutshell.

@undefined Write down, on paper, a definition of the site's intended audience.

undefined

12:47

@PM2Ring thanks, PM 2Ring. Yes of course there is a difference. And there are different types of migration. I dont see a problem with having different types of migration. Because, at least for me, there are different types of migration. Some types are valued higher than others

Emilio Pisanty

> Some types are valued higher than others

wow

basically, you're saying "some types of people (you know, the wealthy, well-educated ones) deserve an SE site for their migration-related questions, the other types don't"

undefined

I think that everyone can ask questions of this SE as long as they're ontopic. But I have seen migration related questions are a better fit on the travel SE for example. I think most people think of something different than migration when they hear/read expat

Emilio Pisanty

@undefined so your site is for all migration-related questions?

if not, then what is it for?

undefined

I think a bit of confusion or misunderstanding is also caused by that, for me, migration also include the group of refugees, which I would never put in the expat group

@EmilioPisanty are you referring to the site I mentioned yesterday? expat.com?

Emilio Pisanty

@undefined so the site is for people who move from one country to another, but you don't want it to be welcoming to refugees or their questions?

undefined

12:55

not welcoming is too harsh. But I just dont think of refugees, when I read expats

I think expats just have very different questions/topics than migrants/refugees

Emilio Pisanty

... and therefore they need this safe Rich Boys' Club where they can ask those questions and discuss those topics away from the ugly migrants and refugees?

anyways

@undefined I misread your comment yesterday. I thought you were referring to expatriates.stackexchange.com, but apparently not. That changes things from "SE hosts site with a racist and classist name" to "SE user participates in an external site with a racist and classist name"

I think the former is pretty scandalous and needs to be changed

undefined

@EmilioPisanty basically yes. Even your wording is too harsh. Those are just two (very) different groups of people. With different needs, different questions and so on.

Emilio Pisanty

What other platforms do or don't do isn't my concern. If you want to participate in classist platforms, go right ahead.

@undefined Of course it sounds harsh. I'm sorry if a realistic lens on the situation uncovers aspects that bother you.

undefined

@EmilioPisanty its doesn't bother me, it's just not right/correct in my opinion.

Emilio Pisanty

@undefined and yet you've been unable to produce any argument against that understanding stronger than "I don't like it"

but like I said

if you want to participate in classist platforms outside of SE, go right ahead

user8718165

13:01

@JohnRennie Hello sir,

Emilio Pisanty

@user8718165 That's beyond the level of insistence that's appropriate for this chatroom.

John has already seen (or will see when he logs in) your messages.

If he doesn't answer, then he doesn't answer.

Shing

Feynman said for a very long wavelength photon, that photon can be scattered into $D_1$ from hole 2 (by a passing electron). For a very short one, that's impossible. I do not understand why a short wavelength photon can't do that, would anyone be kind enough to explain that a bit to me?

ch3, vol3 Feynman's lecture

undefined

I'm not unable but unfortunately my English skills are not high enough to really express all the things I would like to say.
But to summarize, expat is for me just a term to describe a group of people. Like any other term to describe a group of people. And yes, of course, every group exclude some people. there is no one group fits all, for me. And, I'm sorry, but if people feel offended because they dont belong to a group they would like to, thats not the problem of the group. I mean, for example I cant just say "I want to be part of the group of PhD". Because I'm not a PhD. But I cant blam…

user55789

13:33

Howdy all, anyone good at the mathematical side of things?

I'm a bit stuck

Note: the problem is a bit annoying

xd

Emilio Pisanty

@user55789 Don't ask about asking, just ask

user55789

Fair enough, I want to solve the Lieb Liniger integral equation in the cleanest way

So I have my Fermi Rapidity defined implicitly

$$N = \int_{-\lambda_F}^{\lambda_F} \rho(\lambda) d\lambda$$

For a root density $\rho$ satisfying integral equation

$$\rho(\lambda) + \int_{-\infty}^\infty d\lambda' \rho(\lambda') \mathcal{C}(\lambda-\lambda') = (2\pi)^{-1} - \rho_h(\lambda)$$

The ground state case reduces to a simpler equation by picking an empty hole root distribution $\rho_h(\lambda)=0$. Still, these equations, to my eye, appear to have been defined in terms of each other (No?). Numerical approximation of the ground state equation seem to be dependent on the chosen interval of integration

So again, I feel a bit stuck

Emilio Pisanty

oooofff. That looks outside my expertise.

sounds like a question for main

but maybe it's a better fit for the maths or scicomp sites

user55789

Perhaps somebody *can elucidate this:

The thermodynamic case discussed here assumes large N,L in a ratio N/L of unity. Except, it also discusses a definite chosen N for the system which in turn defines Fermi rapidity $\lambda_F$. How does that work?

Should I assume that the equations hold for thermodynamically large values of $N$ only? So the implicit equation for Fermi rapidity $\lambda_F$ holds assuming e.g. $N\gg 1$, for example $N=200$ or something?

And as such it is a limiting case and not an exact equality?

PM 2Ring

16:00

@JohnRennie An easier way to edit chat posts on a desktop computer is to hit the up arrow key. Multiple hits take you to earlier posts if they're still editable.

Emilio Pisanty

@JohnRennie ooooh, ouch

John Rennie

@EmilioPisanty :-)

Emilio Pisanty

(said in the voice of Jimmy McNulty when he returns to the homicide office in season two, just after they take the murders. For those who know what that means.)

PM 2Ring

Is there a decent dupe target for this? Her core conceptual question is how to resolve vectors into X & Y components, but it's hard to tell what she does & doesn't understand. I guess it would help if she posted a diagram.

enumaris

16:22

whew...assembled my sofa yesterday...very non-trivial task lol

user280247

16:43

Since the Coulomb potential V is invariant under translations, then the eigenfunctions of the translation–invariant Hamiltonian operator are not square integrable. What does it mean the last part of the sentence?

user351417

@enumaris Everyone I know hates the word 'nontrivial' so much; they call me a condescending git when I use it :(

user280247

Should I say: why those eigenf are not square integrable?

user351417

@PM2Ring I'm so sure that OP asked the same question yesterday. Gimme a minute

enumaris

@Chair lol

user351417

@PM2Ring physics.stackexchange.com/q/466067 is a perfect duplicate target, but I can't flag it because it doesn't have an upvoted/accepted answer.

user280247

16:45

I think I got it

PM 2Ring

@Chair Ah. I didn't realise it was a self-dupe. I cleaned up the new version a bit. She's naughty for posting the dupe, but I guess she doesn't know you're not supposed to do that.

user351417

@PM2Ring I'll peek about a bit for a duplicate to link though. I'm sure I've seen that kind of stuff before.

PM 2Ring

Yes, it's homework, but she isn't asking for the solution. She just needs a push in the right direction re vector resolution.

user351417

In the meanwhile, I'm sure this one is a duplicate, because I distinctly remember answering it in a test a while back, so it's clearly quite a popular question :P

PM 2Ring

It can be hard finding decent dupes for really basic stuff, especially when you're not sure of the OP's skill level. But I assume she wouldn't have this as homework without some basic trig knowledge.

user351417

16:54

I would not rephrase it because it is fact, until proven otherwise. Besides NASA, who can be criticized because it is government, what other evidence is there that a rocket would work in space? — Jsphappy 2 mins ago

PM 2Ring

@Chair And the OP is a conspiracy theorist. Maybe even a flat earther... Ninja'd

user351417

Lol

user351417

I was just about to say that I'm stepping out of that conversation too :P

user351417

That is one disappointing starboard.

PM 2Ring

16:57

Yeah, I'm not interested in wasting energy searching for info to help people with that sort of attitude. Even a perfect explanation won't satisfy them if it clashes with their preconceptions.

@Chair Dear ROs, some pruning of the starboard may be in order... ;)

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