The h Bar

1:30 AM

1

Q: Calculation of exponential of momentum operator

I'm puzzling out the way one can determine $exp(iA)$ operator for an unbounded $A$. More precisely I would like to know, how could I deal with the momentum operator $p_x = -i\hbar\partial_x$. I'm trying to follow the instruction which I learned from Frederic Schullers lectures (https://www.youtu...

@ACuriousMind do you want to leave a helpful comment or should I drop a bomb

ACuriousMind

@0ßelö7 Why don't you leave a helpful comment? :P

I think all I might want to comment is "see Reed/Simon" :P

0ßelö7

@ACuriousMind Because he's doing 1960s spectral theory and I want to interrogate him as to why

@ACuriousMind Have you actually looked at Reed and Simon?

ACuriousMind

Well, I agree with ZtH's comments that context is lacking for this question

@0ßelö7 Long enough to confirm that Borel functional calculus and all that jazz is actually in there, and no longer :P

0ßelö7

Riesz functional calculus

I went to a talk where a guy was doing something crazier, the usual functional calculus didn't work well with what he was doing

I was missing some context because he just seemed insane

@ACuriousMind He states very clearly that he is looking for the easiest way to rigorously define exp iP

Phase

@Avantgarde Death grips is great

@0ßelö7 a long list of reasons

about as long as the dumb / poorly formed questions I ask here on a daily basis

0ßelö7

1:37 AM

@Phase I don't know how to respond to self-deprecating comments like that.

Phase

its not really self deprecating man its just honest

come on be honest

I make people roll their eyes most of the time RIP

0ßelö7

I never roll my eyes at your doubts, I can assure you.

Phase

Like the other day when I was asking if a matrix was the square root of I as if it was actually uniquely defined

0ßelö7

Square root of a matrix is tricky.

Phase

Anyhoo

ACuriousMind

1:38 AM

@Phase Well, and now you learned that it isn't!

Phase

how'd that proof thing go?

ACuriousMind

I don't see anything wrong with that

0ßelö7

what proof

Phase

@ACuriousMind indeed! I guess my issue is that to me I think I should be learning at a faster pace.

@0ßelö7 the thing you were talking about a while ago? The one that involved a 'more general lemma'

Didn't really get involved at the time, just curious if it's going well or not

0ßelö7

@ACuriousMind Did I tell you about my disastrous attempted meeting with our hyperbolic PDE guru?

@Phase I have a bad memory. Unless you give more context I have no clue what you're talking about

I'm usually stuck on a few proofs at any given time

Phase

1:40 AM

Oh. Well I guess if it's that trivial then nevermind, probably went well and I'm glad : P

ACuriousMind

@Phase I do think you need to be less hard on yourself. Yes, your questions are often confused, but you usually can be made to understand what was wrong with them and learn something in the process. I've seen far worse.

0ßelö7

yesterday, by 0ßelö7

@ACuriousMind I was actually hoping to give a full proof of the lemma, because it's folklore

this?

ACuriousMind

@0ßelö7 If that guru is the Russian lady, then I read your account of that meeting, yes

0ßelö7

@ACuriousMind What do you make of it? Something lost in translation?

Phase

@ACuriousMind yeah I've been told I judge a bit harshly but tbf it's not like I'm comparing myself to geniuses, I just believe I should make more progress because I feel like if I don't it's just mediocre. At least when I start Uni a week I'll have a chance for actual structured learning

Here's hoping having metrics to actually gauge if I'm cruddy or not helps : P

0ßelö7

1:43 AM

So you haven't been at university?

You're too cryptic for us to follow.

Phase

Well, not quite no

it's not important tho

ACuriousMind

@0ßelö7 Sounded just like an old crotchety prof to me :P

0ßelö7

OP should check the standard references: Reed and Simon (volumes I and II), Hall (Quantum Theory for Mathematicians), etc. — 0ßelö7 3 mins ago

@ACuriousMind Happy?

Bernardo Meurer

Breaking the x86 Instruction Set

►

0ßelö7

oh my god

the rain is coming tomorrow

where the hell is my umbrella

@BernardoMeurer getting hit by part of the hurricane tomorrow

Bernardo Meurer

1:51 AM

@0ßelö7 Awesome!

Go swim

0ßelö7

I might be in for a swim

and it's going to rain through the night so I can't wait it out either

Phase

How much of the Hurricane is gonna hit?

Hopefully nowhere near as bad as Florida

0ßelö7

Just torrential rains

Phase

This is Marvellous

Secret

Not so crazy google search inspired from the crazy combination of time travel + self submitting and writing script + numerical analysis:

Augmented Lagrangian method

Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective; the difference is that the augmented Lagrangian method adds yet another term, designed to mimic a Lagrange multiplier. The augmented Lagrangian is not the same as the method of Lagrange multipliers. Viewed differently, the unconstrained objective is the Lagrangian of the constrained problem, with an additional penalty...

The details of the crazy stuff will available later: Self updating lagrangians and action functional

0ßelö7

2:09 AM

@Phase found my umbrella

Phase

2:22 AM

@0ßelö7 maybe rename yourself to something that likes water

vzn

2:51 AM

@Phase lol think youre really only an amateur at that. & think you have some outstanding questions on QM. if only you really cared about the answers :P which reminds me of this, ever heard of it? :) en.wikipedia.org/wiki/Shoshin

0ßelö7

@Jasper ;_; math.cornell.edu/~lsc/iso-rev.pdf

why are all of the papers I'm interested in written in French

I'm gonna start calling manifolds varieties

GPhys

3:29 AM

hmmm i.imgur.com/f9Dwhwd.png

I want to believe it's zero

0ßelö7

@GPhys Is that the energy momentum tensor

GPhys

nope just some arbitrary tensor defined for a problem on tensor manipulations

0ßelö7

It's zero regardless

do $\beta\leftrightarrow \gamma$ and see where that takes you

GPhys

because of the symmetric/antisymmetric thing I assumed it's zero

0ßelö7

@GPhys yes, to prove that, do $\beta\leftrightarrow\gamma$ and set the things equal to each other

then manipulate the indices a bit

GPhys

3:41 AM

@0ßelö7 what manipulations? :< (really the only way I knew how to do this was actually calculating it, but then I barely had enough intuition to guess it was zero)

0ßelö7

@GPhys Skyrim one sec

@GPhys do you agree that $T_{a(b}T_{c)d}T^{[bc]}=T_{a(c}T_{b)d}T^{[cb]}$?

GPhys

Yes

since you're just swapping the indices and they're otherwise just scalars

0ßelö7

so the RHS $=-T_{a(c}T_{b)d}T^{[bc]}$?

GPhys

mmmm

yes

0ßelö7

use the definition of $[cb]$

GPhys

3:48 AM

right

0ßelö7

@GPhys which $=-T_{a(b}T_{c)d}T^{[bc]}$

GPhys

ah so -blah=blah so blah=0

0ßelö7

yes

(assuming a field with characteristic $\ne 2$)

GPhys

adds manipulating the index inside the symmetric/antisymmetric part to toolset

0ßelö7

@GPhys just read appendices B, C, and D of wald if you want to learn index notation

do every calculation

you will be good after that

for Stokes theorem see physics.stackexchange.com/questions/237458/… (seriously)

Wald says wrong stuff

GPhys

3:56 AM

okay I will look, we are using Carroll

0ßelö7

you mentioned that before

I'm not too familiar with Carroll

Wald is a standard for mathematical people

GPhys

that was the easy question at least, the other easy-looking one asks for the all-covariant and all-contravariant components of the levi-civita tensor in spherical coordinates (R^3)

0ßelö7

lmao

there's a formula

(if you know linear algebra)

It's involves some determinants

GPhys

I found det(g)= $r^4\sin^2\theta$

and I think I worked out the formula in terms of that, just convincing myself I'm correct right now :P

Secret

Need to revise how to change basis in tensors

probably multiplying it with some suitable change of basis tensor

0ßelö7

4:07 AM

@Secret why? It's not something one really ever needs

Secret

Probably thinking too much about components and linear algebra...

But it does make me wonder...

If we are doing some calculation in one coordinate system and need to transform the result to another, there should be a way to do so?

e.g. going from rindler coordinates to schwartzchild coordinates after calculating some frame depending quantity at the vicinity of black holes

because if everytime we want to translate coordinate dependent results from one frame to another, it seems very annoying to recalculate everything when we switch coordinate systems

But actually, I am not sure, given how under coordinate transformations, the christoffel symbols do have a lot of nonlinear partial derivative terms

so perhaps recalculating the result is just as intensive as simply transforming it

user228700

4:33 AM

@JohnR: YES, I was able to book a train ticket back to Kerala!

Balarka Sen

@0ßelö7 did you see the new pewdiepie drama

it's kind of serious this time lol

GPhys

@0ßelö7 get to figure out this one yet, but these are just getting into normal Linear Algebra i.imgur.com/qge6Vu1.png

John Rennie

@Kaumudi.H Good :-) At least the journey back won't be too painful.

GPhys

pretty sure for the remaining questions as long as I can convert whatever he's asking to usual maths Linear Algebra language I can figure them out

0ßelö7

@BalarkaSen i did

Balarka Sen

4:43 AM

racist is not a good adjective to be put in front of you, especially when you're already a nazi

bet this's gonna cause major defamation

user228700

@JohnRennie Not at all! :-) AC too!

0ßelö7

@BalarkaSen I don't think saying that word makes you racist

user228700

@BalarkaSen Man, what's happened now? :-/

Balarka Sen

@0ßelö7 I agree.

But the way he delivered it is going to give him hard time

John Rennie

@Kaumudi.H if you must know

Balarka Sen

4:46 AM

@Kaumudi he said the n-word on live stream, in a way that might be perceived in a derogatory fashion

0ßelö7

@BalarkaSen rinku?

user228700

That man.

Balarka Sen

@0ßelö7 what?

0ßelö7

@BalarkaSen Am I racist because my first thought is "so?"

@BalarkaSen oh, you're too young

do you have a link to the vid

Balarka Sen

@0ßelö7 shrug man

0ßelö7

4:48 AM

@BalarkaSen I watched the video

Balarka Sen

which one

0ßelö7

where he says it

Balarka Sen

ah

well it's everywhere

0ßelö7

harmless, but people are going to go apeshit

user228700

@JohnRennie Thank you, BTW :-)

0ßelö7

4:49 AM

do people really not understand the difference between saying a slur when playing a game and going on hate marches

Balarka Sen

@0ßelö7 whether or not it's harmless is debatable, i don't have any opinions on this. i would watch the drama though

0ßelö7

idk about other people, but that was a pretty common word when I grew up -- in both countries

@BalarkaSen it's a word.

vzn

lol pewdiepie + disney, accident waiting to happen! :o o_O :P vzn1.wordpress.com/2017/03/06/…

Balarka Sen

@0ßelö7 sure

0ßelö7

Crap, I forgot to copy my PDE notes to the correct notebook

user228700

4:52 AM

@JohnR: Chocolate ice cream for breakfast, BTW! :-) I'm LTD!

Balarka Sen

i don't get triggered by the n-word but i do think the style of how he said it might come off as offensive to people

0ßelö7

@BalarkaSen I find it hard to believe that anyone is legitimately hurt by a word said in a non-racist context

How he said it? He wasn't chanting it at a Nazi rally

John Rennie

@Kaumudi.H eat drink and be merry for tomorrow we ~~die~~ go back to college :-(

Balarka Sen

like idubbbzTV's slogan is literally "n-word f-word" which I find pretty amusing

but i can't root on the harmlessness on this one

vzn

@0ßelö7 ps whos that in your av?

user228700

4:54 AM

@0ßelö7 I don't think that it is possible for me to have a proper conversation about this but I am interested to know how one is to know that it was a non-racist context.

Balarka Sen

shrugs man. i would just sit out and watch the drama

0ßelö7

@Kaumudi.H wait is it sunday?

user228700

@0ßelö7 Monday here.

0ßelö7

@Kaumudi.H He was playing a video game

vzn

@Kaumudi.H piediepie is like an internet comedian. did anyone hear of andrew dice clay? not much )( difference.

0ßelö7

4:54 AM

@vzn I can't say. People would flag it.

Balarka Sen

I mean he was playing a videogame

vzn

@0ßelö7 ?!? its just some dude right? celebrity? not pewdiepie?

0ßelö7

@BalarkaSen Louis CK says it on stage all the time

@vzn His name is a combination of two slurs

@JohnRennie is allowed to say one of them

Balarka Sen

looool

you m-f m-f n-f

0ßelö7

but that's because it's a food in the City of England

John Rennie

4:56 AM

@0ßelö7 @0ßelö7 someone flagged this post. Want be to delete it?

0ßelö7

@JohnRennie ...

John Rennie

Oops, not sure why there are two links there ...

0ßelö7

This chat is insane

vzn

@0ßelö7 lol you have at least 1 thing in common with pewdiepie. always testing/ pushing the boundaries :P

Balarka Sen

hahah

user228700

4:56 AM

@0ßelö7 Right, how does that make it any different from using racial slur in other everyday contexts?

Balarka Sen

rip

John Rennie

Ok never mind the flag has cleared so presumably the flag was marked invalid.

0ßelö7

@vzn I don't believe in the concept

Balarka Sen

@Kaumudi Look, using the n-word doesn't make it racist; Pewd's delivery was a bit weird sounding to me

vzn

@0ßelö7 lol yeah right mr boundarypusher

Secret

4:57 AM

actu.epfl.ch/news/…

Balarka Sen

It's true that the word has been a racist slur for 300 years but people can use it in non derogatory fashions too

Secret

An LHC upgrade with scitillation fibres to track the trajectory of particles to reconstruct their initial states

0ßelö7

@Kaumudi.H If it's not directed to someone of that race, it's not a racial slur. Context matters.

Secret

but won't prolonged exposure will damage them?

vzn

@Secret ?!? yikes physics wtf :P

user228700

4:58 AM

Hmm. Having experienced no racism myself, I can't possibly comment on whether someone who has would be offended by it.

GPhys

these hints are more mysterious than the questions themselves

Balarka Sen

@0ßelö7 i dunno you can argue P said it as if he was offending the sniper there lol

John Rennie

@0ßelö7 the point is that pewdiepie uses the work nigger in a derogatory way. He clearly wasn't being complimentary when he used t.

Balarka Sen

and then news articles will go off on a tangent that if he slips the n-word in a derogatory way on live streams you never know if he uses it publicly in real life that way

vzn

@Kaumudi.H not too familiar but wasnt gandhi partly all about racism issues?

John Rennie

5:00 AM

He is calling someone a nigger specifically to insult them.

Balarka Sen

That's mostly my beef with that word there

user228700

@vzn Well, yes, in some sense, but that is no longer a going concern.

Balarka Sen

But yeah I have no strong opinions on this either way. I am going to watch the drama for the week though

vzn

@Kaumudi.H unf racism is deep in human nature and evopsych studies confirm it...

user228700

@vzn Erm, what point are you attempting to make, exactly? :-P

vzn

5:04 AM

@Kaumudi.H uh wait, there needs to be a point? o_O

user228700

O_O

Balarka Sen

Uh, 0celo got chat-banned

How strange

user228700

Wtf.

vzn

this idea of "using words/ slurs in a (non)derogatory way" reminds me of weird concept of so-called "reclaiming"...

user228700

Wokay, I'm going to eat some more ice cream and watch some videos created by this absolutely magnificent channel for a while.

Balarka Sen

5:06 AM

I need ice creams

but I don't have one

Secret

It is interesting to note how the concept "racism" is itself controversial within philosophical circles

user228700

You need plural ice creamS? :-P

vzn

@Kaumudi.H ah yes if only 0ce stuck to math 100% of the time instead of 99.5% hed be safe.

Balarka Sen

@Kaumudi.H If I click that will I find Vsauce? I don't want to click on cancerous channels

user228700

@BalarkaSen Jesus Christ, man.

user228700

5:12 AM

No, you will find a channel centered around abstract Math, called Infinite Series.

Balarka Sen

oic

Is math related to science though?

I want 0% Vsauce on this

user228700

No, man, I can guarantee that the vibe of this channel is completely different from Vsauce.

user228700

Why dya dislike his channel so passionately?

user228700

@BalarkaSen Oh, my.

vzn

@Kaumudi.H (thx) :) its some cool stuff what do you watch/ like there anyway

user228700

5:16 AM

Lol, np :-)

Balarka Sen

@Kaumudi.H He's a cancerous meme

user228700

@Balarka: Oh, BTW, that channel had me discover the fact that if I do pursue CN, I will need to learn a heck of a lot of Topology.

vzn

@BalarkaSen lol uh let me guess... video of crystal meth production?

Balarka Sen

@Kaumudi.H Cool!

user228700

Video in question:

Balarka Sen

5:18 AM

I actually heard of some topological robotics while talking to a guy in the workshop

user228700

Your Brain as Math - Part 1 | Infinite Series

►

Balarka Sen

Maybe that's relevant

user228700

@BalarkaSen Oh, wow!

user228700

On a related note, I also happened to read this article about the advent of A.I and it blew my mind just a little.

user228700

Law of Accelerating Returns etc.

Balarka Sen

5:21 AM

Is neural networks at all related to cognitive neuroscience?

user228700

@BalarkaSen Lol, yes, 100%.

Balarka Sen

Ok, then you'll probably face lots of cool math

user228700

Yes, I will! :-D I'm excited!

Balarka Sen

You should teach that stuff to me

user228700

Oh, I'm sure that you will be learning even more advanced crap at C.M.I.

Balarka Sen

5:23 AM

Not cognitive neuroscience surely

user228700

Ah, right, no.

user228700

@BalarkaSen Surely, when I get there in a few years' time.

Balarka Sen

@Kaumudi.H Ah yes I know this one

user228700

The video or the concept?

Balarka Sen

The discovery and a little bit about the math behind it

There's some nontrivial topological ideas involved there

user228700

5:26 AM

Cool! When I discovered the video, I wasn't in a place to pay full attention to it, because of which I didn't watch it till the end and saved it for later. Later is now.

user228700

PBS sponsors some great shows on YouTube, BTW.

0ßelö7

@GPhys post doubts and I will see in the morning

Bye everyone.

user228700

Bye :-)

GPhys

has no idea what is going on

John Rennie

Goodnight :-)

Balarka Sen

5:30 AM

@Kaumudi.H Nice. If you want I can tell you a bit about what homology actually is (which I suspect shows up in the video).

That's how they detected 11 dimensionality of whatever simplicial complex (generalization of "graph") they came up with

0ßelö7

@GPhys what

GPhys

with these questions, I mean :D

0ßelö7

Ok so put your doubts here and I will take a look if you want

GPhys

this one I'm not even sure how to do what he wants even if I could show the hint i.imgur.com/qge6Vu1.png so I moved onto the other ones for now

0ßelö7

Ok I don't know why I'm still up

GPhys

5:35 AM

on this one I'm still trying to understand his map :D i.imgur.com/ChFeq93.png

0ßelö7

Any math questions can likely be answered by @BalarkaSen

@GPhys V is a vector. Awful notation.

Ok sleep 4 realsies now

GPhys

but e_(1) isn't though?

er

Bernardo Meurer

Halp

What's the english word for when one has the control of a field

In the current geopolitical arena, where the main battle is for technological ...

@JohnRennie Use your british powers

GPhys

yeah just trying to understand what $\mathbf{g}(V,e_{(1)})$ is

John Rennie

@BernardoMeurer where the main battle is for technological supremacy

Bernardo Meurer

5:43 AM

@JohnRennie Exactly

You're the man

John Rennie

In my day schoolchildren were taught to speak proper!! :-)

Bernardo Meurer

I was super excited because I though my college essay was free theme-wise

But it's about the worth of college

and I had some super nice ideas on an essay about death

So now I'm struggling to get this done in the next hour for delivery

Anonymous

Anonymous

Can someone understand what's going on here? ^

Anonymous

Particle in a one-dimensional lattice

In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the crystal creating an electromagnetic field so electrons are subject to a regular potential inside the lattice. This is an extension of the free electron model that assumes zero potential inside the lattice. == Problem definition == When talking about solid materials, the discussion is mainly around crystals - periodic lattices. Here we will discuss a 1D lattice of positive ions. Assuming the spa...

Anonymous

5:47 AM

$$\beta^2-\alpha^2=\frac{2m(V_o-2|E|)}{\hbar^2}$$

Anonymous

And not $$\beta^2-\alpha^2=\frac{2m(V_o)}{\hbar^2}$$

Anonymous

@BalarkaSen Could you help? :P ^ Some weird mathy stuff going on

Secret

These days I mostly reside in maths chat because I don't have much physics to discuss. Interestingly, the spontaneous response probability also drops with that, thus the lack of the feedback loop result in increased residence time in the maths chat

The residence time in h bar will rise again once I get back to quantum

Bernardo Meurer

6:36 AM

@JohnRennie Synonym for "Personal growth"?

John Rennie

@BernardoMeurer Why not just say personal development? I can't think of a synonym that does any better.

Bernardo Meurer

@JohnRennie That's what I just did :P

@JohnRennie They told me to conclude with a "thoughtful concluding sentence" so I ended with "As said sir Mix-a-lot ``I like big butts, and I can't deny'' "

John Rennie

:-)

What's the context? What are you writing?

Balarka Sen

@Blue I can't figure out what the symbols are

@BernardoMeurer "England is my city"

Bernardo Meurer

@JohnRennie About whether college is worth it's cost

John Rennie

6:47 AM

@BernardoMeurer bear in mind they have seen thousands of examples of students attempting to be witty ...

Bernardo Meurer

What? I do like big butts!

And I can't deny it!

John Rennie

Unless you are a comic genius I'd be inclined to write something fairly anodyne and straightforward.

Bernardo Meurer

I know, I know, I'm just fooling around

I'll come up with a "thoughtful concluding statement" in the next couple minutes

Balarka Sen

"Marx debunked the idea of university education YEAAAARS AGO!!! FOREVER RESIST CAPITALISM BABY"

Bernardo Meurer

Ended with

"The choice of getting a degree is under more fire now than ever before, and yet it is still intrinsically valuable. Graduating is an enlightening and molding experience, that has shaped many of great women and men of this nation. "

W/e

Balarka Sen

6:56 AM

i see some wahmen respecting there

Bernardo Meurer

What?

Balarka Sen

do you not know the respect wahmen memes

come on man

Bernardo Meurer

I'm old

Aaaaah