The way seems correct to me @Kaumudi.H

the mathematical way is ok!

np

Last night dream someone asked a weird question on PSE, and Leaky Lun's reply is as follows:

$$\sqrt{\frac{x}{y}}:\frac{x}{y\otimes \lvert 0\rangle} < \frac{y}{x\otimes \lvert 0\rangle}$$

Interestingly after I woke up momentarily, the second dream continued saying that only the reciprocals of the stuff in the inequality makes sense

@Kaumudi.H They are computing differentials, and presumably the functions f,v,u are all single variable

e.g. x

This kind of computation is common in experimental error calculations

it is part of the notion of total differential

Ok what I mean is that $\frac{-2}{f^2}df$ is the error term to first order for the function $\frac{2}{f}$

@Kaumudi.H do you not know what a differential is

you compute the derivative then stick on a d(whatever)

it won't make sense until a 5th course in calculus

maybe a 4th

or a 7th

idk

something with manifolds

Each error term can be approximated by a taylor series, thus the linear term is what we called 1st order

and is given by the 1st total differential

I have no idea what you're on about

intuitively, you're just computing a small difference

so $df=f(x+dx)-f(x)=f'(x)dx$

etc.

yup and that's what we called a total differential

so d(dependent variable)=derivative * d(independent variable)

interpreting what that dx really means takes some work

@Kaumudi.H And if there are multiple variables you sum over the contributions.

and thus give you things like the multivariable chain rule

@Kaumudi.H that seems rather straightforward, what is the doubt?

I need to get chatjax on linux

I'm the average stupid user

how the hell does chatjax work

ah, there

I think calculus is one of those things where if you approach it from physics, you can understand the formal manipulations easily

the dirty proofs and rigorous definitions cannot be understood so easily though

but "calculus" just means the formal manipulations

Yeah, to get rigorous and justifying some of the concepts such as differentials such that it becomes analysis, a bag of machinery need to be introduced which is usually too much for average experimental physics and engineering uses

things like topology, continuity, limits, manifolds and so on

see, I don't think manifolds are fundamental to analysis

and to be frank, since I have not studied manifolds yet, I am not very familiar with differentials in a manifold setting

it pisses me off when analysis books stick in manifolds at the end as an afterthought

I guess... analysis don't need to always deal with non eucledian geometry, thus manifolds are not always included, but again I am not an expert on that...

analysis is the study of vector spaces that have topologies

well...and measures.

but disregarding that...

I'm so sick of UFO questions on astro SE

@JohnRennie I need some heroin

fortran is killing me

They still teach Fortran in this day and age?

yes

I suppose there are still millions of lines of Fortran in everyday use ...

it's pretty awful

the I/O is from the days when "print" meant "on a piece of paper"

It is if not one of the worst languages of all time then close to it

@JohnRennie behind cobol it is the best language for GDP

@0ßelö7 only because there is so much of it still around.

oh my god so many errors

fml

how is that not valid, fortran

To be fair I believe the latest versions of the language are somewhat improved. I first used it in 1980 and in those days it was truly diabolical.

the errors make absolutely no sense

it doesn't like that I declared M to be an integer

why the hell not??

and it says I didn't declare a variable except I did in the line right above

sobs

@JohnRennie Jesus Christ, can I not declare inside of a case selector?

now it insists that i is square root of negative 1

what the HELL

@Kaumudi.H Yes, I'll certainly keep an eye open for the book. Do you know what it's going to be called, and the publication date?

@JohnRennie oh my GOD

one has to use the write command to change the format string for the print command

is suicide honorable when faced with fortran?

Might as well, it'll kill you anyway :-)

????????

is this supposed to make sense

ahahahahah I did it

@BernardoMeurer to get fortran to understand format = "(M(X2, I1, A, I1, A, I2))" I had to do write (format, '("(", I1, "(2X, I1, A, I1, A, I2))")') M and also limit format to 80 characters because FORTRAN puts an infinite number of blank spaces otherwise

worst language ever

but it works

@JohnRennie why does gamma equal 1+2/f?

where gamma = Cp/Cv is the heat capacity ratio of an ideal gas, and f is the degree of freedom

@LeakyNun Notice that $C_p = dU/dT$ where $U$ is the internal energy of a unit mol of the gas. By equipartition of unity $U = f \cdot RT/2$. Now differentiate, use $C_v = C_p - R$ and take ratio.

It's a formal computation. The crucial fact is equipartition of energy, which I never quite grokked.

why Cv = Cp - R?

That follows from first law of thermodynamics, if I remember right. Also I meant $C_v = dU/dT$.

quora.com/What-is-Cp-Cv-R

A question: "it helps lexicographers to gain ____ to linguistic data". Should it be " access" or "insight"?

Access, surely?

I thought so too. Some of my friends claim it to be "insight"

Yeah. They are obviously wrong

@LeakyNun Yeah, if I heat up $V$ amount of gas so that the temperature increases by $dT$, and I counteract the expansion (say, volume increases by $dV$) of the gas by some exterior pressure $p$, then the total work is done by the force applied from the exterior is $pdV$. The internal energy increases by $dU = C_v dT$ (that's what specific heat means!), and the amount of heat we're applying is $\delta Q = C_p dT$.

Plug these in the first law of thermodynamics: $\delta Q = dU + pdV$ (modulo errors on my part).

Damn I remember these lol

hmm

equipartition of unity?

did you do too much abstract algebra lol

partition of unity is topology d00d

lol

Well, the first partial is taken at constant pressure, second is taken at constant volume.

I don't see the relation between pressure and enthalpy though

why is Cp defined to be that?

You mean why we compute heat capacity at constant pressure?

I mean why Cp = dQ/dT

reiterate the definition of Cp

specific heat taken at constant pressure?

@LeakyNun heat capacity is always $dQ/dT$.

then what is dU/dT?

But at constant pressure the volume changes so some of the $dQ$ you put in goes into doing work instead of raising the temperature of the gas.

@Leaky I mean this comes from $H = mcT$

Just the infinitisimal version of that

At constant volume no work is done so all the $dQ$ goes into raising the temperature.

If no work is done $dQ = dU$ so $dQ/dT$ and $dU/dT$ are the same.

hmm

U=Q+W right

please, proper notation.

the 1st principle of thermodynamics is about 1-forms

stop using topology terms :c

"1-form" is diff geo not topology

its just symplectic topology tho

>_>

hm i wonder if nlab has anything to say about thermodynamics

AH it does

meh not interesting

where are the infinity categories

@BalarkaSen stop using those whatever category topology diff geo

This is one of the most rubbish answers I've ever posted and people keep upvoting it. That's the HNQ for you.

@JohnRennie are you asking for downvotes?

@Mithrandir24601 I'm not asking for any votes, but I find myself faintly embarrassed by the whole thing. I posted it as a quick answer in between doing two things that I should have done several days ago. And now I find it's accepted and has 21 upvotes. And lots of comments saying it isn't an answer, which it isn't.

@Sid that's because I discovered I can exchange my rep for BitCoin :-)

(this may not be entirely true)

I saw yesterday that heat capacity of a diatomic gaz rises up to 7/2R at high temperatures. Using the equipartition theorem one could very well explain 3/2 (translation) or 5/2 (trans. + rot.) but what are the additional dof from 7/2? I can only imagine vibration between them but would be only one additional dof, no?

@JohnRennie can you delete it and get yourself a shiny bronze badge?

In fact I can't delete it. Once an answer is accepted it's impossible for the OP to delete it. I'd have to ping the person asking the question and ask them to unaccept it.

@Felix.C each vibrational DOF contributes R not R/2

@JohnRennie I know, that's what I'm asking :) Translation, rotation and vibration are imho 6 dof's. So with the equipartition theorem this would result in 3R = 6/2R. But heat capacity goes up to 7/2R. So I wonder if classical mechanics has an answer for this

E.g. what is the 7th degree of freedom, if there is one?

@Felix.C in effect the KE and PE are separate degrees of freedom and you get R/2 for both

I think, though I wouldn't swear to it, that more precisely the vibration is a quadratic degree of freedom and when you work through the equipartition stuff you find these get twice as much energy as a linear DOF.

@JohnRennie Isn't it that ONLY quadratic dof's contribute to eq. theo. At least translation, rotation are quadratic and vibration are quadratic I guess. But PE seems to me as being no quadratic dof though...Thanks anyway for the KE, PE thing..this would explain it in some way.

Hmm, yes, I must be thinking of something else.

It's definitely the KE + PE thing though

@Kaumudi.H Aha. Thanks :-)

Ah, it isn't listed on Amazon yet. I guess it's still too early.

@Kaumudi.H pish and tosh!

Let me see what I have in my pile of bits.

hey @JohnRennie care to dip into review for a minute? physics.stackexchange.com/review/low-quality-posts/189472

@EmilioPisanty Hmm, that's a rubbish answer. What are you suggesting? Vote to delete?

I did vote to delete and ... it's gone! :-)

@JohnRennie I was suggesting that you review as you see fit ;-)

on one hand, it's nice to see the 20k deletion ability actually pulling its weight

but, on the other hand, it is just you, me and Kyle on just about all of 'em

which is... less great

Deleting answers is somewhat controversial, but if I would be embarrassed to have someone I respect read an answer then I will vote to delete!

@JohnRennie Deleting salvageable answers is controversial, but I contend that the bottom of the barrel is not.

Agreed :-)

What we do need are self-correction mechanisms for when content is unduly deleted

Hi @JohnRennie

@Fawad Afternoon

I think my physics teacher was teaching wrong and I need some clarification from you

i.e. the ideal case would see the bottom-of-the-barrel posts deleted by a variety of different users (i.e. not just the same three faces every time), and a healthy population of people regularly checking the 10k tools for any deletions that cross the line

but we're not there yet

@Fawad Yes?

When certain charges are removed from x and put on y, final number of charge on x will be $1\mu-ne$ and final number of charges on y will be $1\mu+ne$ right?wrong?

I haven't used schrodinger formalism in a while so could someone maybe look over my Answer and warn me if I've given OP false info?

Morning

mornin

@Fawad: I calculate the initial force, the force before any electrons are moved, so be an attractive force of 89.9N. Do we aggree on that?

@JohnRennie yes. I got that. Let’s take approx 90N for easy calculation.

And for a force of 360N we need 2e-6C on each object

So you have to transfer 1e-6C charge from X to Y

@JohnRennie how?

@Fawad How what? How do we calculate the charge has to be 2uC?

@EmilioPisanty I'm not sure how many of our 10k users check the tools at all

@JohnRennie sorry I am dumbest person alive. I don’t get what you want to say

@EmilioPisanty Well... technically, everything you cast a delete vote on probably belongs in the VLQ review queue for one reason or another.

So the self-correction mechanism should simply be the VLQ review

@Fawad The question says the final force is 360N. Yes?

Yes. So final $q_1q_2=4*10^{14}$ @JohnRennie

$$ F = \frac{1}{4\pi\epsilon_0}{q_1 q_2}{r^2}$$ so $$q_1 q_1 = 4\pi \epsilon_0 r^2 F$$ Yes?

Yes

$$ = 4\pi \times 8.85\text{E-12} \times 0.01^2 \times 360 = 4\text{E-12} $$

+E don’t work with mathjax. 10^

I know, I'm too lazy to put in all the powers of 10 :-)

LOL

I am too lazy to type 'text'.

The point is that $q_1 q_2 = 4 \times 10^{-12}$, so $q_1 = 2 \times 10^{-6}$ and $q_2 = -2 \times 10^{-6}$

@JohnRennie :/

@Jasper at first I just typed the E-12 without the \text, but then I discovered it didn't format properly so I had to go back and put the \text in. It would probably have been easier to just use the proper notation :-)

When charge removed from x and put on y, they both have same amount of charge? (q1=q2=2*10^-6)

X starts with +1uC and Y starts with -1uC. So |q_x| = |q_y|.

@JohnRennie and while calculating final force?

Am I the only person who finds it funny that "Fawad" is asking questions about EM? x)

@Phase Yes, because r and w aren't that close :P

God damn it ACM stop ruining my fun :C

That was nice lol

@Fawad if we take a charge of $-e$ off X then X becomes more positive by $e$. So now q_x = +(1+e)uC and q_y = -(1+e)uC. The magnitude of the charges remains the same.

^^^^^^^^^ New favourite H bar member

Excellent timing John :D

Also, the pronunciations of the letter A in Fawad and Farad are different.

@Phase my, that's nice of you to say so :-)

@Fawad you appreciate awful jokes though, so you're good in my book

Are we doing electrostatics here or babbling aimlessly about puns on names?

@JohnRennie damn

Idk... is the stress giving you... indigestion..?

@Phase now there's a joke I haven't heard before :-)

@ACuriousMind well, that's what I've been saying all along, but the official position was always a stern "no"

particularly via @DavidZ

hang on ill try inventing a new one

but I don't think that the VLQ works as a review mechanism for deletions that already happened

@JohnRennie that’s what I wanted to know. Thanks :)

@Phase I've already heard all the jokes about my surname that are funny as well as lots that aren't.

tbh

What jokes ARE there besides the obvious

I can't even think of any

@JohnRennie I can't even think of one, lol.

The annoying thing is that it was my family that had invented the popular indigestion tablet I'd probably be a millionaire :-)

Yeah. If its any consolation my surname is pretty jokeable too

More so, even

"Peel"

Since we have descended to making jokes about µFawads and indigestion, now seems a good time to head off and get lunch.

@JohnRennie careful you don't eat too much and earn yourself some heartburn

Emilio Pissant-y

@Phase yeah, you're definitely the first one to come up with that one

although that joke sounds harsher than I wanted

RIP sorry Emilio

@Phase that too

Emilio Pi-santa

there we go

that's more friendly

It's a nice feeling actually finally contributing to this site instead of just being a tumour and asking tumourous questions

oh my god

the brits can't even spell tumor right?

nice bait mate

nevermind

Im still a tumour

I wrote that you find the eigenvalue, and then you can find the eigenfunction with the schrodinger equation

but that isnt right is it

The eigenfunction is the eigenvector that goes with the eigenvalue

So what's the solution to the SE? Just an eigenfunction OF the SE?

@0ßelö7 please help I want at least one constructive post on this site

busy

@Phase which SE? TISE or TDSE?

@EmilioPisanty This is my answer

and why do you think there's "the" solution to the SE, as opposed to "one" solution of the SE?

Well the solution is a family of functions for the infinite well of a certain form

@Phase yeah, I saw that, mostly I thought the question was too puddly to have an answer to begin with

@Phase solution to which equation?

ill just delete it

Solution to the TISE

@Phase I don't think there was anything wrong in there

Yeah but if its not a question that belongs on the site there shouldn't be an answer I guess

@Phase I don't think it's bad enough that it needs to not get any answers

well now I am torn

if your answer isn't wrong and it helps OP then I say sure, w/e

Can answers be undeleted at any point or are they dropped after a certain time since deletion?

though then again this is a good bit of word salad

> Consider the infinite potential well, The solution to this gives you the complex probability amplitude function which can be multiplied with its conjugate to give you a real function describing the probability of finding the particle at various points in the well.

> The energy eigenvalue corresponding to some pure Energy state now also corresponds to some eigenfunction solution to the differential equation, so you now have functions describing the probability of finding the particle dependent on the Energy state it's in.

it is? I thought it was all defined terminology

my understanding of word salad is meaningless words thrown together, I was just trying to keep it concise and have all the words be there for a reason

:(

@Phase you can undelete at any time, but deleted answers can become undiscoverable after a set time. If you have the URL you can always see it and if you can see it you can undelete it (if you deleted it yourself) but it will only be listed in your profile for sixty (?) days. After 10k rep you can search for your deleted posts though.

Fair. whats word salad about it tho

@Phase Mostly, I don't think it's clear enough to be useful. I still can't quite work out what you're trying to say.

Well, that the solution to the SE gives you a complex valued function that represents the probability amplitude, and you take $\psi \psi *$ to get the real valued function $P(x)$

And the second paragraph refers to states where the state isn't a sum of eigenfunctions / is only composed of one eigenfunction, and that that function is a solution of TISE that is related to its own unique energy eigenvalue [as long as it's not degenerate]

and wrapping it up by saying that those functions then describe the probability of the particle as a function of where in the box it is