The h Bar

A more interesting question would be the physical consequences of different representations. I recall that locality breaks in the momentum representation

ZeroTheHero

5:09 AM

I seem to recall that some nuclear potentials are sensitive to momenta and yes that causes problems, although locality is the least of your worries in this case.

oh! I should add that the gravitational potential is also linear..

GodotMisogi

@ZeroTheHero Possible typo? You've written $V(x)\psi(p) \to ik\hbar\frac{\mathrm d}{\mathrm dp}\psi(p)$. Shouldn't it be $V(x)\psi(x)$?

ZeroTheHero

well when you use the momentum representation your wavefunctions are p-dependent...

I mean: $\hat x$ acts on functions of $p$ by derivative.

GodotMisogi

Oh, I've been reading it as (position space) → (momentum space)

So, in general, $V(x)\psi(x) \mapsto V(i\hbar \frac{\mathrm d}{\mathrm dp})\psi(p)$

ZeroTheHero

The more accurate statement would be that
$\langle p\vert V(x)\vert\psi\rangle= V(i\hbar d/dp)\langle p\vert\psi\rangle$

After all one determines if you are in the $x$- or $p-$ representation by closing with either $\langle x\vert$ or $\langle p\vert$. The ket $\vert\psi\rangle$ is just a vector and doesn't care about the basis.

anyways I have to prep for the morning classes.

TTFN

GodotMisogi

I understand. I think I misunderstood the presentation as eigenfunction representations on both sides

Anonymous

9:39 AM

Motl's on our site!

Anonymous

2

A: Optimal strategy to a quantum state game

We simply translate the binary result of a qubit measurement to our guess whether it's the first state or the second, calculate the probability of success for every possible measurement of the qubit, and then more find the maximum of a function of two variables (on the two-sphere). First, someth...

Anonymous

Could we get any more publicity than this? :P

Slereah

Praise be

Physics Meta

0

Q: How can "torus shape" planet be "non-mainstream" physics?

Refer to this question: How would the rotational and orbital mechanics differ on a torus-shaped planet as compared to a spherical planet? This is asking about torus-shaped planet rotational and orbital mechanics. To me this is a question can be answered completely using Newtonian physics, and i...

Anonymous

@Slereah We've both Duffield and Motl now. Our site's going places. :)

Slereah

9:44 AM

Time to sink that ship

Secret

10:25 AM

23

Q: sed on OSX insert at a certain line

So I've been using 'sed' on linux for a while, but have had a bit of difficulty trying to use it on OSX since 'POSIX sed' and 'GNU sed' have so many little differences. Currently I'm struggling with how to insert a line of text after a certain line number. (in this case, line 4) On linux I woul...

sed osx posix gnu

ffs stop saying sed. It is useless in macs

Whoever came up POSIX should be thrown into a blackhole

John Rennie

@johndecker Hi, what's the question?

johndecker

I want to learn about solving PDEs on curved surfaces.
For example, the 2d wave equation on a sphere: tap the north pole, a wave spreads with decreasing amplitude to the equator, then the amplitude should increase again as the wave continues past the equator toward the south pole. This is different from solving the 3d wave equation and then narrowing the solution to a spherical surface.
I believe there’s a rule “replace derivatives with covariant derivatives” in the PDF. Is that it?
Where do I study this? Textbooks? Online lecture notes? Examples?

(Culix suggested I post here, as it's supposed to be a helpful chat room.)

John Rennie

@johndecker that's a bit outside my comfort zone, but yes using the covariant derivative sounds a plausible approach.

The area of maths involved is differential geometry

In fact it's the same maths as used in general relativity, and for the same reason - solving equations on a curved manifold.

johndecker

10:41 AM

@JohnRennie, exactly. I've studied introductory differential geometry and GR, but the textbooks I have only solve trajectories (geodesics), not PDEs (except Einstein's equations themselves which solve for the geometry, not classical fields IN that geometry).

John Rennie

I think it's a general principle that any differential equation on a Euclidean space can be applied to a curved manifold just be replacing derivatives by covariant derivatives. The results can get a bit messy though.

The Christoffel symbols for a 2-sphere are pretty simple though.

bolbteppa

11:21 AM

It's amazing that most of the issues Lisi failed to understand/understand-properly, e.g. the $SU(5) \times SU(5)$, $F_4 \times G_2$ subgroups of $E_8$ or $E_8$ and it's real reps motls.blogspot.com/2007/11/exceptionally-simple-theory-of.html , are in GSW's string book, but Lisi kept bashing strings so clearly never checked the usual reference for this stuff

John Rennie

11:33 AM

Ideally we should put the works of the blogosphere physicists behind us and get on with physics that is actually fun and interesting.

2

Physics Meta

0

Q: Why can't I suggest "Chemistry Stack Exchange" as another site when flagging as off-topic?

I've recently noticed that when I flag something as off-topic by suggesting it to another site(in order to get better answers for that question) I only see the options of Physics Meta Stack Exchange and Mathematics Stack Exchange (shown below in the picture), like no Chemistry Stack Exchange or B...

feature-request flagging

Slereah

12:13 PM

@johndecker Try Friedlander maybe

amazon.com/…

user351417

12:54 PM

2

user351417

@Blue Does that look strange or what?

Slereah

1:29 PM

that noob

Novalium Company

1:48 PM

When we solve definite integrals, in what (I forgot the word) do we get the area? In meters squared or in cm square...?

mathsisfun.com/calculus/integration-definite.html Here they just get a number for the area, but is it $m^2$, or maybe $cm^2$?

Maybe it's $banana^2$ xD

user2723984

well it depends on what units you use to measure your $x$ and $y$

if $x$ is meters and $y=f(x)$ is meters too then $f(x)\mathrm{d}x$ is $m^2$

Novalium Company

@user2723984 Thx.

user351417

2:04 PM

@NovaliumCompany Indeed, if your $x$ and $y$ axes both have units '$\rm bananas$', you will actually find the integral as '$\rm bananas^2$'.

bolbteppa

2:21 PM

rob

2:41 PM

-1

Q: If the jerk is 2, then acceleration is 2t, velocity is $t^2$ and distance is $t^{3}/3$?

Are my graphs and equations right? I just began learning about these..

kinematics jerk

I case a "homework-like" close vote there, but I'm having second thoughts: it looks more like "playing around" that I'd prefer we encourage. Any thoughts from others?

I think the photograph threw me off, and I would have parsed it differently if it'd been typeset.

user351417

3:34 PM

physics.stackexchange.com/questions/457220 Yikes! There were 5 answers, including upvoted ones there!

Anonymous

@Chair Oops! SE is broken. ;)

rob

@Chair User removed for violating system restrictions. The removal script deletes negatively-scored content.

user351417

@rob That's a pity, because the answer which was highest scored at the time I last looked was quite different from all the answers in that and the duplicate.

user351417

Is a merge or something possible?

Physics Meta

3:55 PM

0

Q: Notification to the user whose comment is deleted

I strongly believe that a user, whose comment is deleted by a moderator should be notified about it. Many moderators ask the user to remove their comments however some just remove them without informing the user at all.

feature-request

enumaris

4:38 PM

fun times

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