The h Bar

12:12 AM

-1

If gravity travels at the speed of light what is it that prevents something with mass entering a black hole not to achieve light speed?

The OP thinks with Newton and in the newtonian version, something coming from infinite will go with c on the event horizon and yet faster below that. Instead of closing the question, the correct answer would be to explain, what happen on the GR.

DanielSank

@ChrisWhite what's going on in the second code box of this SO post's accepted answer?

@BernardMeurer

Bernard Meurer

@ChrisWhite Hopefully you'll be able to help us out :v

0celo7

@BernardMeurer I'm praying to the book with the cool cover but it's not helping me

This problem is insanely difficult for some reason

Bernard Meurer

@0celo7 Books written by Brazilian writers will only help you if you dance half naked while you have a beer with one hand and pray with the other

it's our native ritual

0celo7

No beer I'm afraid

dmckee

12:16 AM

@MikaelKuisma The person who wrote that comment is making a rather technical claim about which theories provide a definition of "photon". Photons can be—and routinely are—used in a plain QM context, but you have to simply assume a set of properties for them. Field theory derives the properties from the second quantization procedure.

Bernard Meurer

@dmckee Maybe you can help, check DS's link please

1-800-D-MCKEE

0celo7

REEEEEEE

Mikael Kuisma

@DanielSank Looks very weird to me. I would expect compile error, but then again, c++ has weird properties.

0celo7

Just got a quote for a piece of software that's $20,000

Bernard Meurer

@MikaelKuisma That's pure C, not C++

dmckee

12:19 AM

The daughter class is defined as a structure including the parent class. (Aside, you could implement either "is a" or "has a" inheritance this way). It makes the access semantics for properties of the parent class nasty, but that can be hidden behind an opaque interface if you have the discipline.

0celo7

FML I had the wrong ODE

Mikael Kuisma

@dmckee That is rather my understanding as well (about the persons claim and photons in general).

0celo7

@SirCumference I did the chain rule wrong ;_;

there goes the last two hours or work

Bernard Meurer

@dmckee How is shape_computeArea(&r1) leading to float rectangle_computeArea(const ShapeClass *shape) in his final example?

dmckee

Frankly, OOP-in-C is not something to mess with until you are very comfortable with he internals of the language and have at least a little practice with pointers-to-functions.

Mikael Kuisma

12:22 AM

@BernardMeurer Ah, I think I understand what's going on now, on second glance.

dmckee

@BernardMeurer Your initializing routine for shape_rectangle has to assign a pointer to rectangle_computeArea to the shape.computeArea member of the included struct.

You really want to hide the nastiness behind a bunch of opaque help routines.

Really.

Bernard Meurer

@dmckee Oh god, what a spaghetti

Thanks by the way :)

Does polymorphism work on this kind of implementation?

0celo7

Maybe I need some results on Killing vectors

dmckee

Uh, that business of assigning pointer-to-function is the basis of getting some basic polymoprhism working.

Bernard Meurer

@dmckee Seems hard to debug

dmckee

12:27 AM

It worth recaling that the earliest versions of C++ were just re-writers on top of C, so anything that you could do in C++ in, say, 1990 is possible in C with only a lot of pain.

Mikael Kuisma

one can make OOP code with assembler as well. So anything will work in code like C where you can be really loose on memory access and typing, but...

dmckee

@BernardMeurer No one promised it would be easy. You probably want to get in the business of code generation for the boilerplate.

But by then you are half-way to re-implementing C++...

Bernard Meurer

@MikaelKuisma I got shivers when you said "OOP in assembly"

Please never say that again :p

Mikael Kuisma

drdobbs.com/embedded-systems/…

Bernard Meurer

@MikaelKuisma Traumatized for life

Sir Cumference

12:37 AM

@0celo7 Two hours O_O

0celo7

Been working for about 4 today on this problem

I was trying to get information out of the ODE $c'=\alpha'(v-Jv)$, but I made a mistake in deriving it

Sir Cumference

Dang

I feel that

0celo7

It's really like

$c'=\alpha' v-\alpha'\alpha/\beta\cdot Jv$?

Not nice

I've made almost no progress, this is so frustrating.

DanielSank

@MikaelKuisma It's not C++.

Mikael Kuisma

I know the feeling. I have been doing this one derivation for few weeks now.

DanielSank

12:42 AM

@dmckee @ChrisWhite I understand that code now.

Wow, I really learned something here.

Mikael Kuisma

@DanielSank Yes, I completely misunderstood it at first.

DanielSank

You really can make classes and polymorphism work in C, you just have to do a lot more typing than you would in C++ :)

@dmckee Yeah this is the critical part. Very clever.

Mikael Kuisma

I prefer python. Or C. C++ is somehow not nice.

DanielSank

@dmckee Yeah that's called C++ :D

dmckee

At one point the dillo browser project was using OOP in C, and I submitted bug reports and a patch. But I never went near the OOP code. Scary stuff.

Physics Guy

12:51 AM

@Ocelo7 What does ODE stand for ?

0celo7

Ordinary differential equation

DanielSank

@BernardMeurer Yeah, it does.

0celo7

@MikaelKuisma I'm reading a book on Ricci flow. I don't know much about PDEs, so I can accept results in that domain on faith. But there's this page of geometry that's stopped me dead in my tracks since Saturday. I have literally no clue what's going on and that's so frustrating because I know a lot of Riemannian geometry.

I might have to hunt down Hamilton's original paper, but I really don't want to give up

It seems like a neat exercise, honestly

But the more I think about this problem, the more frustrated I get

And I can verify that the solution works, but I don't see why that particular solution works

I think an ODE has to appear somewhere

Mikael Kuisma

Solving a matrix ODE is what I have been lately frustrated about. Very simple stuff, but so frustrating.

0celo7

But it has to be a second order one

And even if I find the magical first order ODE that I need, I don't know what the initial conditions should be

Physics Guy

1:01 AM

Why dont you do something else then ? Riemann Hypothesis will get you more frustrated ;)

Mikael Kuisma

Unfortunately I cannot help you with that, I don't know nothing about that topic.

0celo7

Well, I know what they should be because I know what the answer is

I don't know how to get it

@MikaelKuisma I'm not holding my breath for my prof knowing it either

Physics Guy

Are you working on a specific excercise or do you just calculate a bit ?

0celo7

It seems deceptively simple

@PhysicsGuy I'm working on a proof

Of a theorem in the text

Physics Guy

What theorem ?

tell us

0celo7

1:03 AM

It's in the chat above.

I'm on my phone now, not going to retype it.

Physics Guy

Okay.

I dont want to search that chat section, now.

0celo7

Although I do have the problem memorized...

Physics Guy

@Ocelo7 hey, but if you want to work on Riemann surfaces later, you can use these papers (there are excercises), but it is in german (you said you could speak german):

esaga.uni-due.de/ulrich.terstiege/Lehre/RF

0celo7

Thanks

vzn

1:31 AM

@DanielSank joking? :(

@JohnDuffield similar eqn in fluid dynamics iirc en.wikipedia.org/wiki/Electromagnetic_wave_equation

0celo7

Still no progress

I thought taking a break would help

DanielSank

2:52 AM

@vzn Teasing @ACuriousMind.

But I think he had a rough day around here.

user54412

@DanielSank My special power: getting people's questions answered by being absent for long enough that things resolve themselves.

2

user54412

Thanks, HNQ, I'm now listening to Old English samples on youtube.

DanielSank

3:19 AM

@ChrisWhite I hadn't seen an example of polymorphism in C before.

Pretty neat.

DanielSank

3:31 AM

Gives you an idea of how polymorphism really works in the C++ compiler.

vzn

3:42 AM

4 hours ago, by DanielSank

@ACuriousMind all those theories/experiments/ideas which about the elasticity/permeability/etc of spacetime It would be cool if someone would explain this as I'm sure it could be interesting or new and might shed light into string theory.

↑ oh yeah that would be so way cool d00d, bet it will be chock full of lotz of EQUATIONZ plz let me know asap if you run across that & will personally pay to fedex it overnight intl shipping to ACM

DanielSank

@vzn hahahahahahaha

vzn

@DanielSank did they cover permeability in your phd classes? (you dont seem like a string theory type)

vzn

3:57 AM

Jul 13 '15 at 21:26, by 0celo7

↑ working on ur problemz

@ACuriousMind hint: velocity of sound in an ideal gas + dimensional analysis

user54412

4:59 AM

It's @JohnRennie

user54412

Is today for saving the servers, synthesizing colloids, or just teaching the youth about ~~heresy~~ GR?

John Rennie

Morning

Right now it's six a.m. and the no. 1 priority is coffee :-)

I have had a look at the servers and all 528 of them appear to be running sweetly (says John frantically touching wood)

Secret

5:34 AM

8 hours ago, by ACuriousMind

Or the pressure at the Earth's core will rise slightly.

The pitfall of abusing dimensional analysis=have not think through what the outcome physically mean in relation to the other variables used in the dimensional analysis

Secret

5:51 AM

[AI mode] I wonder, if there are any h barers that are more in tune with the way I think like most people I met in real life so that if I have another question on something, they will be able to help me to translate it in terms they understood...?

William Bulmer seems like a good candidate...

[technobabble] Now that he's back, the matrix should be stablised somewhat to carry out the plan...

goodreads.com/quotes/…

So that's physical intuition...then why are my intuition often end up like word salad...?

7 hours ago, by William Bulmer

@vzn I don't think dimesnional analysis ever suffices as a valid physical argument for why something should be true. As I had said, I think it is more helpful as a compass for finding deeper physical/mathematical relationships

First thing to ask yourself when doing a dimensional analysis: Is the bunch of units you obtained in the end really have the physical meaning you expect them to be...?

DanielSank

@vzn No idea what you mean.

Secret

6:10 AM

7 hours ago, by ACuriousMind

@vzn Oh yes, I've seen that "analogy" from JD many times until I began to ignore him. "Elasticity" is a well-defined notion in continuum mechanics of materials, but it's not a well-defined notion w.r.t. spacetime, at least not in GR. It doesn't actually mean anything to say that "spacetime is elastic", and it doesn't mean anything to say that light is "distortion of spacetime" because there are no equations that would allow that interpretation.

7 hours ago, by vzn

@ACuriousMind did you see JDs eqn/ analogy or not? speed of light, permissivity/ permittivity of free space etc... nearly same as what WB is "poynting" at :P

7 hours ago, by ACuriousMind

@vzn I don't know what "elastic property of spacetime" means, or why you would call lightwaves a "small scale distortion" of spacetime when spacetime is not dynamical in the classical or quantum theorie sof electromagnetism that describe light waves.

7 hours ago, by vzn

@ACuriousMind look, am willing to take a small stab at this/ go out on a limb (for you to immediately saw off...) a lot of eqns point that spacetime itself has a dynamic/ elastic property, and lightwaves are apparently just the small scale distortion of it whereas gravity is the large scale distortion of it. so then, the zen question, how do these two mesh?

reddit.com/r/askscience/comments/18zpsd/…

Here's a problem: How do we define any notion that spacetime has a young modulus, as johnrennie point out in a discussion recently

If we cannot ,then spacetime is not a putty like other materials

(NB The posts are placed in reverse chronological order)

and then you also have that counterexample mentioned by Slereah about the O(forgot) name) metric

You know things are not looking good if a blue arrow become red, and that's why despite my emotionally volatile nature, I refrain from using much emotional words or words that give people an impression I am challenging others

If there's one thing about negotiation between two worldviews, is that their defense systems make it very hard to sustain a meaningful conversation. Usually worldviews become defensive when a perception of challenging them occurs

One reason why despite my extremely incoherent nature I still have not been consumed by my own pet theories is I try to keep myself open and not let my worldview to judge others (and converse in a way to not make other worldviews judge me)

Most of the time , my worldviews, ladden with numerous pet theories, are often wrong, and I rely on others to point me to the correct direction

Secret

6:33 AM

arxiv.org/pdf/1603.07655.pdf

(To authors) Explain Slereah's counterexample (more accurately the Ozsváth–Schücking metric) with your model

(Will let those interested to have a peek at it as I am currently not GR focused in study yet (I am still revising quantum))

(NB2 I cannot find a journal reference)

@ChrisWhite in lagrangian mechanics, what is the motivation that we integrate the lagrangian wrt time and define this functional as the action, but we don't have motivation to define something similar by integrating the lagrangian wrt the generalised coordinates or momenta?

Secret

7:06 AM

0

Q: Gravity in the Riemannian Universe

I was reading about the Riemannian Universe http://gregegan.customer.netspace.net.au/ORTHOGONAL/00/PM.html I noticed that Greg Egan doesn't seem to talk about how Gravity would work in the Riemannian Universe. For Galilean Relativity there is Newtons Law of Gravity and for Lorentzian Relativity...

physics gravity relativity

(Protip: There is basically no one on h bar in Syd time 15:00-21:00)

Secret

12:47 PM

0celo7

use $\gg$

\gg

Secret

ok, noted, will use that in the future

0celo7

also $\ll$ \ll

Secret

Caption: A weird result observed when playing Quantum Moves:
If the wavefunction is oscillating, then when the well suddenly moved to a new location, and that new location is where the wavefunction was somewhere up the wall of the well's original location, then it is possible to concentrate the wavefunction near the middle of the new well

Using naive intuition, it might be kind similar to how when you slosh water around in a bowl, if you jut the bowl in a way to against where it is sloshing (similar to the principle of playing a swing but instead trying to stop it), then the water will slo…

David Z

1:24 PM

If anyone wants to add an item to the agenda for the chat session, ping me about it. So far we have two items up for discussion, corresponding to the two featured meta posts. History questions and the VLQ flag experiment.

0celo7

@DavidZ I'd be interested in talking about differentials of flows which are isometries

If at all possible

Secret

1:45 PM

Jim

@DavidZ I'll probably be away during the chat session. So if it comes to a vote on the vlq flag experiment, I want it known that I'm officially against flagging wrong answers but for flagging non-mainstream answers. If it doesn't come to a vote, just ignore me

0celo7

I take it DZ's silence is a yes?

Jim

Unless you are going to ignore me no matter what, in which case THIS MESSAGE IS IRRELEVANT!

0celo7

In fact, it's excited approval?

Secret

Another weird observation when playing the famous bring home water level.

If your well has the same depth as the target well, and the barrier between the double well just low enough to allow a portion of the wavefunction to reach it, then one half of the doubble well will start drain up completely and fill in the other (and then the whole process reverses and repeats again)

Naive intuition suggest that the wavefunction might be thinking that initially there's only one well and it is not oscillating in position (only in phase), and then we slot in another well with the same energy levels s…

(Also equally interesting, if the well have different depths when forming the double well, the wavefunction will not drain completely)

If the maths agrees with the naive intuition, then it is possible to make a ground state wavfunction to behave like an nth excited state wavfunction as we slot in more wells to make a multi well potential

0celo7

1:51 PM

Hmm

Secret

the game also does not seemed to treat tunneling, I wonder how will that screw it up...?

0celo7

$\nabla_v\xi-av\propto Jv$

wonder if that's useful

Secret

If they actually have take account of tunneling and the maths agrees with the naive intuition,then it brought another interesting question:

If I have an array of wells that are separated by some distance L from each other, and they are all of the same shape and depth (hence their spectrum when considered individually will be identical). Then in the context of the whole well array, there should be a period of oscillation where the initially localised wavefunction will end up "jumping" to other wells in a periodic fashion, determine by the tunneing width of the wells and the initial period o…

This will mean if we have n replicates of a system, if we wait long enough, we will be able to transport the initially localised wavefuncton in well i to well j

and it will still be localised

So by timing the period of this oscillation, we should be able to take this wavefunction intact to any well we want with full fidelity

we can then cut it off with the rest of the wells by isolating it and shift its energy spectrum by deepen the well

Secret

Yet another question can be ponder about is whether a given energy spectrum has a one to one correspondance with the geometry of a well. I.e. will there exists two wells of different shapes such that they have identical energy spectra?

William Bulmer

2:10 PM

Hello, again

David Z

@Jim we never vote in chat

John Duffield

@vzn : I know.

@vzn Space. Not spacetime.

@WilliamBulmer : IMHO it's because at the fundamental level space and energy are the same thing.

0celo7

@JohnDuffield can you please explain what this elastic property is

and give an equation or two that supports it

Physics Guy

@JohnDuffield Where did you take the information that space and energy were the same at fundamental levels ?

John Duffield

@0celo7 : space waves. Look it up.

Physics Guy

2:18 PM

Cause I think thats.....well, you know.

John Duffield

@0celo7 : I did.

Physics Guy

@JohnDuffield Also: the trampoline visualization of GR is incorrect.

2

Well, not incorrect, but it doesnt really show how spacetime is like.

0celo7

@JohnDuffield But the stress energy tensor is an object of the matter fields, not spacetime itself

Physics Guy

@Ocelo7 Exactly

John Duffield

@DanielSank : and Maxwell. But space, not spacetime.

@0celo7 : do your own research.

0celo7

2:22 PM

what

> It is an attribute of matter, radiation, and non-gravitational force fields.

lolololo

John Duffield

@PhysicsGuy : it isn't right, but IMHO it's not as wrong as people think.

0celo7

Literally says the opposite of what you want

Physics Guy

@JohnDuffield Why ?

John Duffield

@PhysicsGuy : I can't give you a reference. But see things like this. When you step up a dimension from the rubber sheet to an "elastic bulk" analogy, the jelly represents both space and energy.

David Z

@0celo7 no, that's not chat session material

John Duffield

2:28 PM

@PhysicsGuy : because the rubber sheet can represent the properties of space in horizontal slice through the Earth and surrounding space.

Secret

https://arxiv.org/pdf/1603.07655.pdf

For all you GR guys to ponder about

NB I suspect it fails for CTC and the pp wave spacetime that slereah mentioned

(PS I cannot do much in chat right now as my current batch of questions are all QM related, thus I need to wait for the QM guys to get on)

0celo7

2:52 PM

@DavidZ says who

Terry Bollinger

3:02 PM

Lively discussion here... :)

0celo7

@TerryBollinger hello

Want to talk about Riemannian geometry?

Terry Bollinger

Hmm... can you tell me something cool or unexpected about Riemannian geometry?

ACuriousMind

@TerryBollinger Hey, how are you? (If you're here for the chat session, you're one hour early)

0celo7

@TerryBollinger No

Cool is subjective

And I'm hopelessly stuck

Terry Bollinger

Drat, did I miss another daylight savings time hour boundary? So, 12 noon EST?

0celo7

3:06 PM

@ACuriousMind Are you willing to listen now or did I piss you off

ACuriousMind

@TerryBollinger It's always at 1600 UTC, can't tell how that translates into your timezone

Terry Bollinger

Heh! I'll leave you two to chat and come back at noon. Nice to see both of you though. I'm working on a fun little SR symmetries paper, just for grins really.

0celo7

SR symmetries?

Terry Bollinger

@0celo7 causality symmetries

0celo7

Ah

It's not easy to show that causal relations are transitive

John Rennie

3:09 PM

At first glance I read that as casualty symmetries :-)

0celo7

that rhymes

ACuriousMind

@0celo7 I can't answer questions about flows, but I'll listen to other technical questions

0celo7

@ACuriousMind I really just need someone to bounce ideas off of...

Maybe there's something extremely obvious I'm missing

@ACuriousMind Let $F:\Omega\times [0,\tau]\to\Bbb R$ be smooth, where $\Omega\subset\Bbb R^n$ is open and $F(x,0)=0$ $\forall x\in\Omega$. Suppose $\partial_t F\le L F+C\tau^{-2}$ on $(0,\tau]$, where $C>0$ is a constant. Why does the maximum principle imply $\sup_\Omega F(\cdot, t)\le C\tau^{-2}t$?

I don't have high hopes for you being able to answer this

:/

Here $L$ is any strictly elliptic operator.

I think one has to just consider $G=F-C\tau^{-2}t$.

Secret

@acuriousmind I have a bundle of questions for you (which will flood your ping inbox very quickly which is why I choose not to ping while you are in Wacken)

Hopefully they will make sense to you apologies for my incoherent thought patterns

To begin with:

Q1. How do we know a photon is not a composite entity made of massless positive and negative charges such that it has some overall nth order multipole moment but neutral. On a related note, do electric charges always come with mass. Is it theoretically allowed to have particles that has charge but no mass?

ACuriousMind

@0celo7 I have no idea what the "maximum principle" is to begin with, so no, I can't answer that :P

0celo7

3:17 PM

Too bad

@ACuriousMind $H^0_{dR}(\Bbb N)$ is just $\prod_{\Bbb N}\Bbb R$, right?

ACuriousMind

@Secret Charged massless particles are allowed. We "know" the photon is not composite because there's no evidence of it being composite.

Secret

What would instead would have been observed if photons somehow has a composite structure?

like what are the experimental signs (that we have not seen, thus we conclude photon is elementary) that would have suggested a photon is composite?

ACuriousMind

@0celo7 If by $\mathbb{N}$ you mean the 0-dimensional manifold with countably many points, then yes.

0celo7

@ACuriousMind Yeah

Call that product $\Bbb R^\omega$

What is $H^0_{dR}(\Bbb N\times\Bbb N)$, then?

I'm trying to see that it's not $\Bbb R^\omega\otimes\Bbb R^\omega$

ACuriousMind

@Secret You're asking the question the wrong way around: Our current theories have the photon as non-composite, and QED matches experiment perfectly. What exactly you expect for a composite photon would heavily depend on what it is composed of

0celo7

3:22 PM

Apparently $H^0_{dR}(\Bbb N\times\Bbb N)$ contains matrices of "infinite rank"

But $\Bbb R^\omega\otimes\Bbb R^\omega$ does not

ACuriousMind

@0celo7 Well, use Künneth, no?

0celo7

@ACuriousMind No, this is a counterexample to Kunneth.

Kunneth only works when one of the cohomologies is finitely generated.

(finite dimensional in the de Rham context)

This is an exercise in Bott & Tu and Hatcher, I'm not crazy.

ACuriousMind

Oh, I didn't know that Künneth doesn't always work.

But isn't $\mathbb{N}\times\mathbb{N}\cong\mathbb{N}$, so the two cohomologies are the same?

0celo7

I'm not sure what $\Bbb R^\omega\otimes\Bbb R^\omega$ is

user54412

@ACuriousMind Can you even have composite things propagating at the speed of light in anything looking like QFT?

Secret

3:28 PM

let's say suppose if the photon was composed of a configuration of charge mentioned above, then it can be an overall electrical neutral object (like the photon we know in real life). I then suspect that one can possibly distinguish between these two photons by checking that it has some nth order multipole moment (where n > 4, thus might not not as easy to measure)

However going along this thought process, I am not sure if there are other possible experimental signs that would be suggested by such composite photon that we otherwise would not have observed

0celo7

@ACuriousMind Trying to use diff invariance of the cohomology?

@ACuriousMind Can we return to this later? I've got to run.

ACuriousMind

@ChrisWhite Well, "composite", i.e. bound states are a bit difficult in QFT to begin with. For instance, trying to predict the low-energy hadron spectrum of QCD is computationally rather intensive and doesn't work all that well, iirc

Considering that glueballs are massive, though, I think you're right that massless composite particles can't occur in ordinary QFT

user54412

I'm just thinking semiclassically -- If a thing is actually moving at the speed of light, its components wouldn't be able to communicate interactions to each other.

user54412

This is the intuition someone once suggested for why two parallel beams of light don't attract each other in GR.

Secret

hmm, using what you guys said, then a composite photon made of massless electric charges might end up being massive instead of massless, and that might break the vacuum solution of maxwell equations

Herr_Mitesch

3:40 PM

Hey everyone :-)

ACuriousMind

@Secret What "vacuum solution"? A massive photon would just wreck the inverse square law, and make the force decay exponentially

@Herr_Mitesch Hi there

Secret

Clarification: By vacuum solution, I am thinking about the electromagnetic wave solution of maxwell eqaution without charge and current density (My knowledge only goes up to classical electrodynamics, thus naturally my thought process move here first)

Ah I see, and since we experimentally measure that exponent to be 2.00something, it is good enough to rule out any composite photon models

Herr_Mitesch

Wouldn't massless particles with some interaction energy look massive from the outside?

Secret

I think a photon's lagrangian does not have any self interaction term...?

Herr_Mitesch

well, of course a photon could have intrinsic higher multipole moments, which would couple it to itself in more complex ways, but those are non-renormalizable anyway, I guess.

ACuriousMind

3:46 PM

Yeah, I'm not convinced that there are consistent QFTs with composite massless particles

John Rennie

@Herr_Mitesch yes they would. A bound state of two massless particles would be massive. For example a glueball is massive.

David Z

OK, our chat session is coming up. Any last additions to the agenda?

John Rennie

Have we got an agenda post we can pin?

David Z

I'll make one shortly

Secret

@ACuriousMind
Q2 leads into Q3: Since a spectrum is just the multiset of eigenvalues of an operator. We should expect that a energy spectrum of a potential well is not uniquely described by the geometry of the well (that is there can be two different types of wells with identical spectrum?)

(Q3 is too big, I will ask later...)

ACuriousMind

3:58 PM

@Secret The question of whether there's a 1:1 correspondence between Hamiltonians and their spectra is asked on this site already. Try to find it.

Secret

ok

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