The h Bar

lılostafa

20:02

@Blue Their similarity is that almost everybody has to take the GRE (for grad school, in the US) just like almost everybody takes the JEE (for IIT, in India).

@JohnRennie I think mom shouldn't be capitalized here neither.

Semiclassical

Quantum question which I should know and it's bothering me.

Anonymous

@lılostafa Well, I suppose SAT would be a better comparison in that case (since high school passouts appear for SAT). But then again, SAT is waaaaayyyy easier. The problem students face in getting admits to the top schools in the US is that they have to show their extra-curriculars,academic achievements like olympiad medals, social service etc. Only SAT is never enough.

0ßelö7

most people have never heard of olympiads

lılostafa

@0ßelö7 True, but (unfortunately) people here (like India) mostly think of olympiad medals as a very great scientific achievement! I hate that.

Semiclassical

The Robertson uncertainty relation states that, if $\hat{A}$ and $\hat{B}$ are Hermitian operators, then the standard deviations of these operators satisfy the bound $\sigma_A\sigma_B \geq \frac12 |\langle [\hat{A},\hat{B}]\rangle|$.

Anonymous

20:08

@0ßelö7 Same here. Very few people actually take part in the olympiads.

Anonymous

JEE is more hyped

0ßelö7

can we please not talk about JEE

Semiclassical

If you take $\hat{A}=\hat{x},$ $\hat{B}=\hat{p}$ then this gives back the usual statement $\sigma_x \sigma_p \geq \frac{\hbar}{2}$.

0ßelö7

@Semiclassical yes

what is $\langle A,B\rangle$ though?

lılostafa

@Blue Do general public in India have more respect for a gold medalist in the international math olympiad or the JEE 1st rank?

Anonymous

20:10

@lılostafa Well, it atleast shows you're hard working and passionate towards that subject if nothing else. I've never heard anyone calling olympiads a "scientific achievement"

0ßelö7

should that not be a commutator

Semiclassical

yeah, fixed

Anonymous

@lılostafa The latter, obviously.

Anonymous

But then most JEE top rankers are olympiad medalists too.

Semiclassical

but, uh, I just figured out where the source of my (as yet unstated) confusion was

so never mind :/

0ßelö7

20:11

hmm, ok

Semiclassical

actually, I might as well say where I was going.

just to make clear why I was wrong :P

lılostafa

@Blue Really? I got respect for JEE then :P

Semiclassical

As a particular special case, take $\hat{A}=\hat{H}$ to be the Hamiltonian of some system and $|E\rangle$ to be an energy eigenstate.

0ßelö7

are you trying to get the time uncertainty principle?

Semiclassical

Nah

this is much simpler and much dumber :P

then $\langle H\rangle =\langle E |H|E\rangle=E$ and $\langle H^2\rangle =E^2$, so $\sigma_{E}=E^2-E^2=0$.

lılostafa

20:14

@Blue Well, I mean I hate it when I see people years after they got these medals or rankings still use them when introducing themselves. things like this.

Semiclassical

which makes sense: you've got a determinate value of $E$, so there's no possibility for variance.

Anonymous

@lılostafa That's strange. Those guys are usually quite humble (from personal experience).

Anonymous

I've never seen anyone boasting about their olympiad medal, lol. :P

Semiclassical

@lılostafa As a way of remembering a certain time in ones life, that kind of thing isn't so strange. But using it as evidence of ones talent is a bit strange.

0ßelö7

@Semiclassical ok

Semiclassical

20:17

the above uncertainty relation would then require that $0\geq \frac12 |\langle [H,A]\rangle|$, and since the RHS is nonnegative real it must be zero.

0ßelö7

stop

Semiclassical

now, is that so strange? ...well, no

0ßelö7

you can have $\sigma_A=\infty$

Semiclassical

sure, but you hardly need to.

0ßelö7

or you accept the fact that your uncertainty principle needs to be more rigorously stated :P

Semiclassical

20:18

The above is perfectly rigorous. There's a proof on Wikipedia.

The principle is not the issue.

0ßelö7

@Semiclassical For finite dimensional Hilbert spaces.

For interesting spaces, it needs to be done more carefully.

Semiclassical

You're making it too complicated. The resolution is just this:

$\langle [H,A]\rangle = \langle E|HA-AH|E\rangle$.

0ßelö7

@Semiclassical I'm actually not, you can "violate" the uncertainty principle because of this. There is an easy counterexample.

lılostafa

@Blue What I said isn't true for everybody, and it usually happens by others (who think too much of these olympiads and exams) rather than themselves. Also, it depends on what you call boasting.

0ßelö7

@Semiclassical Yes

Semiclassical

20:20

ffs. I'm saying why, even if you grant that $\sigma_A$ is finite and that nothing weird is going on, having $\sigma_H=0$ is not a problem.

0ßelö7

I said "yes"

I'm listening

Semiclassical

But $H|E\rangle = E|E\rangle$---it's an eigenstate---and since $\hat{H}$ is Hermitian we also have $\langle E |H=\langle E|E$.

0ßelö7

Ok, I see what you're doing.

Sure, that's fine.

Anonymous

@lılostafa Well, other people do hype about it. Sure. Nothing can be done about that.

Semiclassical

And from that it follows that the expectation of the commutator vanishes.

So there's nothing actually strange about this.

Anonymous

20:22

Other people hype anything they find extraordinary.

0ßelö7

@Semiclassical now read this physics.stackexchange.com/questions/233266/… and explain it to your students

because that is legitimately strange

Semiclassical

ugh, that one

is annoying

0ßelö7

@Semiclassical it's the basis for many careers :P

Semiclassical

I know I've thought about it before, but I can't remember the full of it

I think my usual manner of attack was to consider it as a limiting case of a confining potential.

and argue that we shouldn't be surprised if things go weird when we take the limit

0ßelö7

@Semiclassical That's a physical way of looking at it, I guess

Semiclassical

20:25

this is pretty handwavey, to be sure

Amusingly, the Wiki page I mentioned earlier actually does address this 'counterexample'

0ßelö7

I'm pretty pragmatic about it and simply don't expect $[x,p]$ to make sense everywhere on the Hilbert space

Semiclassical

link

0ßelö7

@Semiclassical I own the book they reference

Semiclassical

Relevant bit: "Although this result appears to violate the Robertson uncertainty principle, the paradox is resolved when we note that $\psi$ is not in the domain of the operator $\hat{A}\hat{B}$, since multiplication by $ \theta$ disrupts the periodic boundary conditions imposed on $\hat {B}$. Thus, the derivation of the Robertson relation, which requires $\hat {A}\hat {B}\psi$ and $\hat {B}\hat {A} \psi$ to be defined, does not apply. "

0ßelö7

yes, I'm aware

that's what I meant by being more careful with the statement

Semiclassical

20:28

Right.

0ßelö7

to be fair, it's correct on a dense subspace of the Hilbert space

so it's almost correct :P

Semiclassical

I do think it's interesting to consider the case where the system is an annulus rather than a straight ring

0ßelö7

it should be generic boundary condition behavior

@Semiclassical I'm gonna do something dangerous and pull a physicist :o

Semiclassical

On the physical side, making it an annulus doesn't change the fact that the angle is restricted to $[0,2\pi)$ and therefore must have finite variance in $\theta$.

So maybe it doesn't help.

0ßelö7

If $H$ is a nonnegative self-adjoint operator I expect that for $\xi\in (0,\infty)$, $$||(H+\xi)^{-1}||\le 1/\xi$$

because $H+\xi$ is larger than $\xi$

seems legit

that might actually be a valid proof lol

@Semiclassical see, it's things like this that I expect someone to have done experimentally

has anyone actually measured HUP violations due to boundary conditions?

Semiclassical

20:34

dunno, haven't read up on it. I know there's a lot that's been done, though.

0ßelö7

8

Q: Does mathematical sloppiness in quantum mechanics ever produce incorrect predictions?

Does mathematical sloppiness in standard quantum mechanics ever produce predictions that don't pan out? I'm not talking about things like the WKB approximation, but instead subtle functional analytic issues, such as assuming every Hamiltonian is self-adjoint, has an eigenbasis of bound states, do...

Semiclassical

I think the way people would interpret the ring example is not so much "HUP is violated" as "HUP is being misused"

lılostafa

Semiclassical

I mean, when we usually think of an observable, it's a real number and as such there's no upper bound on its variance. With the ring case, the observable is only defined mod 2pi.

lılostafa

@Blue Kalpit Veerwa, who secured the 1st rank in SC category of JEE (Advanced) exam, topped the JEE Main exam and created history by scoring 360 out of 360 in the exam ^

Holy shit I'm terrified just by his look :O

Semiclassical

20:38

So the claim might be that one can't equate uncertainty with variance in that case.

Anonymous

Dude, 0celo will kill you for talking about JEE now.

0ßelö7

@Semiclassical yeah

@Semiclassical hmm

Anonymous

@lılostafa Heh?

ACuriousMind

@lılostafa ...is there an "a" missing in the slogan behind him? Because "Educating for better tomorrow" seems ungrammatical

Semiclassical

I think there's probably a better statement than this, though

Educating for better tomorrows?

ACuriousMind

20:40

@Semiclassical Hm...sounds weird to me, but it's possible, yes

Semiclassical

you don't actually see the end of the word, so it could be plural.

google time, methinks

nope, google images has it as just "tomorrow" as well.

Jasper

It could be like a newspaper article title, where articles are omitted

"Dog eats cat which eats bird"

Anonymous

@Jasper lol

ACuriousMind

I dunno, "educating for better tomorrow" sounds...a bit uneducated to me :P

Semiclassical

could also be a slightly faulty translation

0ßelö7

20:44

@Blue no, I just blocked

him

ACuriousMind

@Jasper ...what sort of newspapers are you reading?

0ßelö7

@ACuriousMind implying anyone reads the newspaper anymore

Jasper

@ACuriousMind Zoo news from Mars, not Earth.

0ßelö7

@BalarkaSen wearing sandals and chinos right now and it feels bad

Jasper

@lılostafa I think he has nice hair, that's all.

0ßelö7

20:47

How do you do this

lılostafa

@ACuriousMind Happens a lot

Bought this today ^

Semiclassical

@0ßelö7 hmm, check out equation (1) of this paper and the surrounding sentences: researchgate.net/profile/Miles_Padgett/publication/…

main upshot being that they don't use the usual HUP in trying to handle the case of a photon on a ring

0ßelö7

@yuggib how does one say the Sz in Sz.-Nagy?

@Semiclassical >researchgate

@Semiclassical it ain't loading

says it need to validate my browser

Semiclassical

Weird

0ßelö7

@Semiclassical huh, it was an autodownload that was being blocked

looking now

625 PUBLICATIONS 19,542 CITATIONS

how do you get 625 publications??

@Semiclassical If you know @EmilioPisanty, he would likely have insight here

Semiclassical

21:01

(0_0)

That's a bit much

0ßelö7

what's that face for

Semiclassical

625

0ßelö7

publications or Emilio?

Semiclassical

That's a lot of publications

0ßelö7

@ACuriousMind I am trying to unthaw some pasta sauce my sister in law made for me but it's not happening quickly enough. Should I just throw the brick into a saucepan at low heat?

ACuriousMind

21:03

@0ßelö7 yes, that should work

Semiclassical

Throw it in at high velocity :P

0ßelö7

@Semiclassical with enough kinetic energy it will thaw itself

Semiclassical

Exactly

0ßelö7

wait, is unthaw a word?

or is the word thaw

ACuriousMind

@0ßelö7 "unthaw" would be the same as "freezing", right?

But in a language where flammable and inflammable mean the same thing, I'm not taking any chances :P

0ßelö7

21:04

No sure, is "un" an isomorphism?

un·thaw
ˌənˈTHô/Submit
verb
1.
NORTH AMERICAN
melt or thaw.

lol

Semiclassical

North American English is weird

The "usage" section here for unthaw is funny: en.oxforddictionaries.com/definition/unthaw

0ßelö7

I lost the paper in a sea of tabs

lılostafa

@0ßelö7 The best way is to hold it in water for a few minutes

0ßelö7

@lılostafa it's a decent amount

a few minutes won't do it

@Semiclassical Ah, I see.

The usual example is a bit of a red herring because it's angular momentum masquerading as linear momentum

I guess $\theta$ is a proper observable?

Seems off because it's defined mod 2pi.

Semiclassical

It does seem a bit goofy

ACuriousMind

21:14

@0ßelö7 The conjugate variable to angular momentum has some issues, I think

I think Emilio knows more about that than I, though

0ßelö7

That's why I pinged him

Semiclassical

One easy way to get to a non-goofy version of this is to insist one only worry about the uncertainty in Cartesian coordinates

In that case the observable don't have these mod 2pi issues and everything acts as expected

I'm not sure how satisfying a resolution that is, but it does cordon off the issue

Emilio Pisanty

22:02

@0ßelö7 @Semiclassical what's the action?

0ßelö7

@EmilioPisanty we're wondering about HUP on the circle

Emilio Pisanty

22:26

@0ßelö7 what about it?

I mean, beyond the fact that there's no linear momentum on a ring

0ßelö7

22:38

@EmilioPisanty for starters, what is the conjugate variable to angular momentum on a circle?

Emilio Pisanty

22:58

@0ßelö7 morally? Angle

Technically? Nothing

What, precisely, do you mean by 'conjugate variable'?

(keeping in mind the restrictions imposed by the Stone-von Neumann theorem)

0ßelö7

23:31

@EmilioPisanty Do you mean the von Neumann relations?

0ßelö7

23:48

er

Weyl relations

Bernardo Meurer

Today in Bored Adventures: How many levels of VMs can I do?

Currently at 4

0ßelö7

My coffee has some stuff in it, on the top, and I can see the convection currents

pretty damn neat

Bernardo Meurer

extra caramel jizz?

Hernan Miraola

Does someone want to answer me the next question?

0ßelö7

residue from pasta sauce that I got in it, most likely

Secret

23:58

0

Q: Numerical Tools for Bohmian Mechanics

I am trying to do some simulations using the de Broglie - Bohm formalism and am wondering if there are computational tools that already exist in this area. I generally use Python, but will consider anything, even if I have to put some numerical analysis theory into code.

resource-recommendations computational-physics simulations software bohmian-mechanics

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