The h Bar

Emilio Pisanty

12:13 AM

@AccidentalFourierTransform =P

heather

12:37 AM

@KyleKanos why do you keep accusing me of trolling?

I am doing nothing that resembles trolling.

0celóñe7

@heather link?

skullpatrol

What do you consider to be trolling?

heather

@heather the fact that you 'forgot' your answer and ignore the upvotes in that comment still makes me think you're trolling me — Kyle Kanos 26 mins ago

(except, of course, I didn't forget my answer or ignore the upvotes on the comment.)

or

@heather can't tell if you're trolling me or you are serious and can't follow simple logic. — Kyle Kanos 3 hours ago

here, again, this isn't "simple logic", i really cannot tell the point he is trying to put across.

Read the discussions if you wish. I have been perfectly civil throughout and have not trolled once. I'm trying to have a useful discussion!

Countto10

Impartial observation, I can't believe either of you are trolling types

skullpatrol

@heather wait for Kyle to explain here in the chat room :-)

Looks like miscommunication to me.

heather

12:44 AM

@skullpatrol exactly why I pinged him

hopefully so, yes.

Emilio Pisanty

@heather, if it helps, I don't think this was constructive discussioning

@heather I'd argue that anything more than one is overkill and anything over two is being plain ridiculous. Dupes are dupes, if you can't see that, you should not be reviewing, plain and simple. — Kyle Kanos 24 hours ago

heather

yes, i kind of felt he was being a bit rude. i attempted to ignore that and merely address the actual points.

rob

@heather I always think that your profile image is a candle. It is disorienting when I realize that it is a rocket launching. More disorienting when I vaguely recall having had that realization in the past.

Emilio Pisanty

@rob ditto

heather

@rob i cannot tell you how many people have thought that

Emilio Pisanty

12:47 AM

except for the disorientation part

heather

i keep it now because it's kind of funny how many people don't realize it's a rocket.

(and i don't really mind it being a candle.)

Countto10

@rob please don't mention rocket launches,

rob

Why is that, @Countfrom10?

Emilio Pisanty

Also this was incredibly rude, @KyleKanos. I hope it was simply the result of a bad day and that you can come back with fresh eyes tomorrow.

2

0celóñe7

@rob some people are triggered by tax money going down the drain

Countto10

12:51 AM

Two lunatics with nuclear missiles is not good, even if it's only sabre rattling

rob

@0celóñe7 Surely you mean "up in smoke"? A rocket launch is literally the opposite of "down the drain."

Emilio Pisanty

0celóñe7

@rob That is, if rockets actually go up...

rob

Unless you're thinking of ocean disposal of non-reusable boosters?

Emilio Pisanty

@0celóñe7 ^ much tax dollars

skullpatrol

12:52 AM

chat.stackexchange.com/users/94624/kyle-kanos

0celóñe7

And does SpaceX have absolutely zero subsidies?

Emilio Pisanty

:39359578 I don't follow. How is a private company launching private satellites on private money offensive to people that are concerned about tax dollars?

skullpatrol

He not usually active now @heather

chat.stackexchange.com/users/94624/kyle-kanos

0celóñe7

@EmilioPisanty Tesla is not a private company, are you sure that Musk's other projects are?

heather

well, i'll wait and see what he says, i suppose. i'll have to leave soon myself, anyway.

Countto10

12:53 AM

Well, it's the first time I have heard of one side telling the other exactly what time to expect the bang. May

Emilio Pisanty

@0celóñe7 I'm rather happy to have a constructive discussion about the pros and cons of fixed-cost vs cost-plus contracts in the funding of aerospace technologies. Are you?

0celóñe7

I can't imagine you would find it constructive.

skullpatrol

> ::shots fired::

:P

Cows

guys help . . physics.stackexchange.com/questions/351181/…

final comment is where i am

Avantgarde

@heather 's pic, I agree, doesn't look like a rocket until you look closer. Looks like hands holding a 'diya' to me

Cows

1:05 AM

anyone here knowledgeable about such matters and able to convo?

It is a random thing I want to know a bit about

Kyle Kanos

@heather Because any point I make, you swerved to a new topic to complain about. and conveniently forget what was done previously

@EmilioPisanty Perhaps somewhat rude, but when someone's changing topic with every response, it's hard to have a competent & civil discussion

skullpatrol

Kyle Kanos

1:23 AM

@skullpatrol I think someone else posted that a few days ago

skullpatrol

Perhaps.

Emilio Pisanty

@KyleKanos To be frank, I find all of your comments to heather under your answer to be extremely abrasive, in a way that's completely unwarranted. I do not at all think that heather managed her end of the conversation in the ways that you charge her with, but even if she did, you're better than that - there is simply no need to respond with snark and abrasion.

I say this because this is untypical of you. This is a friendly request: please take some time out and come back in the morning; the internet will keep overnight. You may well come back to find things in a rather different light. If you don't, then fair enough.

Kyle Kanos

(Okay, that's meant as humor there)

I'm probably done with that thread anyway

Not worth my time and effort. I'm okay with the community disagreeing with me, but I think it's the wrong decision.

skullpatrol

There is a "maturity" difference here to consider.

Middle school vs graduate.

Kyle Kanos

@skullpatrol I graduated 2 years ago. I'm a working stiff now

Countto10

1:34 AM

@KyleKanos no, that's good, if my other half saw that, she would identify me immediately

Emilio Pisanty

@KyleKanos precisely ;-)

skullpatrol

She's in grade 9, I think.

Kyle Kanos

Had the internet been a popular thing when I was in 9th grade, I'd have been the worst troll ever

I was a pretty big one when I had it in like 11th grade

Emilio Pisanty

@KyleKanos I'll provide a couple of comments under your answer, since you explicitly asked for them. I do not require a response unless you absolutely want to (and I do not intend to enter into a polemic there; I've said I disagree, I'll explain some reasons why, and that's a perfectly reasonable place to leave things).

Kyle Kanos

@EmilioPisanty ten-four.

Emilio Pisanty

1:37 AM

@KyleKanos say again?

Kyle Kanos

Ten-code

Ten-codes, officially known as ten signals, are brevity codes used to represent common phrases in voice communication, particularly by law enforcement and in Citizens Band (CB) radio transmissions. The codes, developed in 1937 and expanded in 1974 by the Association of Public-Safety Communications Officials-International (APCO), allow brevity and standardization of message traffic. They have historically been widely used by law enforcement officers in North America, but, due to the lack of standardization, in 2006 the U.S. federal government recommended they be discontinued in favor of everyday...

Emilio Pisanty

@KyleKanos a'ight

Kyle Kanos

10-4 (or ten-four) means "Understood"

ACuriousMind

@skullpatrol that's a pretty patronising comment. Please don't judge users by their age, but by their words and actions.

Emilio Pisanty

I guess in all my The Wire re-watches I never paid attention to the actual numbers they were babbling on

Kyle Kanos

1:38 AM

My dad is former military and said things like that all the time

@ACuriousMind Eesh, I probably look horrible to people

Emilio Pisanty

@skullpatrol so? She has a long track record of participation on main, meta and hbar. That's plenty to form an informed opinion of her "maturity level" (if that's what you were burning for) without making blanket assumptions based on her age.

oooooh, @ACuriousMind is here?

Countto10

@@EmilioPisanty no, smokey and the bandit is the movie I vol

Emilio Pisanty

guess who's only two rep-cap days away from the Epic badge?

←

Kyle Kanos

I think I've had like 2 total rep-cap days

Am I able to donate those?

Emilio Pisanty

@KyleKanos don't think so, no

but bounties do count, if what you wanted was to skew that race

Kyle Kanos

1:40 AM

But I just broke 20k! If I did that, I'd lose that mark

Emilio Pisanty

that cone-angle-surface-seeing answer blew up completely out of proportion. four rep-cap days out of it.

Kyle Kanos

I think my rocket answer was one of the 2 rep cap days

Emilio Pisanty

@KyleKanos probably both =P

Kyle Kanos

Possibly, I really don't remember

Emilio Pisanty

@KyleKanos SEDE does, if you don't and you care

but it's better for your mental health not to do the latter

Kyle Kanos

1:44 AM

At some point I realized that I was never going to be as good an answerer as some/most people, but I enjoyed answering nonetheless

ACuriousMind

@EmilioPisanty wow, you really might get that one before me.

Kyle Kanos

So I think most of those rep-based badges just became non-competitions for me

Emilio Pisanty

@ACuriousMind =P

@KyleKanos well, things change

Kyle Kanos

I'm out of the business though ;)

Tough to remember all those derivations from Goldstein and whatnot when you spend your day watching the market

Emilio Pisanty

@KyleKanos (true, that)

Kyle Kanos

1:46 AM

When was Physics.SE started? 2011? 2012?

Emilio Pisanty

that's a graph of my rep-cap days over time

@ACuriousMind's is rather different

skullpatrol

'11

ACuriousMind

@EmilioPisanty well, which HNQ isn't blown out of proportion? ;P

Kyle Kanos

Apparently I've had five rep-cap days

Emilio Pisanty

@ACuriousMind yeah, that's by definition

but still

Kyle Kanos

1:48 AM

2013-10-09,2013-11-28,2014-07-30,2014-08-14,2014-12-16

Emilio Pisanty

mine strikes me with the clustering

Kyle Kanos

@EmilioPisanty Query link?

Emilio Pisanty

often at the beginning of term

@KyleKanos data.stackexchange.com/physics/query/708497/… duh, forgot to link

try user id 1325

Kyle Kanos

Emilio Pisanty

@KyleKanos ?

Kyle Kanos

1:50 AM

Lame

It didn't save the image

There

Mine's pretty epic

Emilio Pisanty

@KyleKanos well, it looks like the beginning of mine ;-)

Kyle Kanos

Yeah, ACM's is definitely looking differently than yours

Emilio Pisanty

@JohnRennie should have a look at his, though =P

skullpatrol

Now that^ is epic.

Kyle Kanos

Is legendary one that's given each time you break the next 200?

Emilio Pisanty

1:54 AM

@skullpatrol you might even call it legendary

2

@KyleKanos no, AFAIR it's only given once, at 150

Kyle Kanos

Okay

Emilio Pisanty

there was talk of multi-awards but if if it's still on the books it hasn't been implemented

not that it would impact anyone other than JR & Lubos

Kyle Kanos

Floris hit 150 in June

skullpatrol

Oops

Emilio Pisanty

@KyleKanos s/he did

Kyle Kanos

1:58 AM

Pretty sure Brandon & I are the only ones with 6 steward badges :)

Emilio Pisanty

his/her progress graph looks pretty linear; naive linear extrapolation puts him/her earning his/her second legendary badge at some point in 2020

@KyleKanos yeah, I kinda gave up on reviewing

I was the second (non-mod) steward badge on closevotes, by a hair, and then I gave up

Kyle Kanos

Brandon & I had a good race to get the Late Answers one, but I figured out the trick before he did & eked out the victory

Emilio Pisanty

@KyleKanos there's a trick?

Kyle Kanos

For Late Answers, sorta

When you notice a 1-rep user answer a question, it takes about 20 minutes to pop up in the Late Answers queue (if it satisfies the other criteria)

skullpatrol

How long were you gone for? @KyleKanos

Kyle Kanos

2:01 AM

So if you pay attention to the main page & watch for 1-rep users posting answers (tab was always open at school) you can judge when it's going to come and get the review in

@skullpatrol I gave up working on the site for a few months, but I mostly comment & review. Answers are few and far between (this weekend was an exception since the wife was away & I got bored a lot)

Emilio Pisanty

@KyleKanos pfffffff

much too much work

Kyle Kanos

@EmilioPisanty But when you're in a race to get all 6 review steward badges, it's worth it

Emilio Pisanty

@KyleKanos yeah, I guess different people gamify differently

-3

A: What is the significance of negative frequency in Fourier transform?

Negative frequency light is purely from our perspective. It is in fact light of a deeper frequency of which ours is a subharmonic terminating in a node of zero hertz.

↑ that guy, for instance, gamifies by... posting bizarre stuff?

skullpatrol

Three months is a good break :-)

Kyle Kanos

@EmilioPisanty Gamifying posting answers that make people confused and/or laugh?

Emilio Pisanty

2:05 AM

@KyleKanos yeah, I guess

skullpatrol

A lot of good people burn out here.

Emilio Pisanty

I gamify most rep given away on bounties, for instance

Kyle Kanos

@EmilioPisanty Interesting: I found a badge I got before you: outspoken

Emilio Pisanty

my current project is making total-rep-I've-given-away get a spot on the first page of all-time rep

Kyle Kanos

I'm still working on getting to the top line of all-time voters

Still have no clue who this Wolpertinger person is: physics.stackexchange.com/users/101770/wolpertinger

But somehow they've managed almost 11k votes

Emilio Pisanty

2:08 AM

@KyleKanos used to go by Numrok iirc

Kyle Kanos

oooooo, I remember that guy

Emilio Pisanty

@Numrok Thanks. It is the action for a black hole spacetime. — user11128 Jan 25 '16 at 20:12

Kyle Kanos

That was fast...

Emilio Pisanty

@KyleKanos google.co.uk/…

skullpatrol

He's a master sniper.

Emilio Pisanty

2:10 AM

the google caches of close statements seal it, though

Kyle Kanos

Ah, makes sense

skullpatrol

I like that username: "master sniper"

Kyle Kanos

Well I've got a long day tomorrow, so i'm going to go to bed now

Emilio Pisanty

@KyleKanos 'night

Kyle Kanos

@EmilioPisanty Goodnight

(and to everyone else)

skullpatrol

2:16 AM

cya

Secret

[The Jonathen curse]

Often when I talk to somebody named Jonathen and is an organic chemist, it is hard to keep up with them because they think faster than I am

I already have two examples of that

skullpatrol

Organic chemistry requires quick thinking.

Take a chunk of coal and synthesis a diamond in as few steps as possible.

skullpatrol

2:44 AM

While in biochem your end product must be a hormone :-)

Mithrandir24601

7:23 AM

@KyleKanos one of my friends from undergrad :)

(Actually the person that got me using SE in the first place)

AccidentalFourierTransform

8:33 AM

Dear Qubitzers, GR=QM, Leonard Susskind

> It is said that general relativity and quantum mechanics are separate subjects that
don’t fit together comfortably. There is a tension, even a contradiction between them—or
so one often hears. I take exception to this view. I think that exactly the opposite is
true. It may be too strong to say that gravity and quantum mechanics are exactly the
same thing, but those of us who are paying attention, may already sense that the two are inseparable, and that neither makes sense without the other.

craaaaaaackpot

ACuriousMind

@AccidentalFourierTransform lol

@AccidentalFourierTransform Saw that. I don't really understand what he's saying except "AdS/CFT is real", but I don't know what that's supposed to have to do with his much stronger statement that quantum mechanics is inextricably linked with gravity

Listening to him, one might think that the only systems that exist are AdS/CFT dual engineered shells of matter :P

AccidentalFourierTransform

Susskind will always be a misunderstood soul

that, or he is a crackpot

lets ask him

u tehre @LeonardSusskind

Leonard Susskind

136 1

ACuriousMind

I take it you agree with my summary then? Or have you completely given up on actual discussion in favour of jokes? :P

AccidentalFourierTransform

I dont understand a word he says in that article, so any attempt at discussion is entirely futile on my end

ACuriousMind

I see. I'm not really following his train of thought there, either.

John Rennie

8:56 AM

To be fair to Prof Susskind he's reached that point where he can think crazy thoughts without jeopardising his career - a luxury not available to younger academics. The chances of the crazy thoughts being directly useful are slim, but in the process of others criticising, maybe deriding, his comments some useful progress might be made.

AccidentalFourierTransform

"a luxury not available to younger academics" excuse me, I can think of crazy thoughts too: I have no career to jeopardise

John Rennie

I can (and do) think crazy thoughts without jeopardising my career. The difference between me and Susskind is that no-one is interested in my crazy thoughts :-)

2

(except possibly the FBI)

ACuriousMind

@JohnRennie Not sure whether that's a reflection on the FBI or on you ;)

Also, shouldn't you have said MI5?

John Rennie

9:13 AM

Aren't MI5 the equivalent of the CIA rather than the FBI?

ACuriousMind

@JohnRennie I thought that was MI6

John Rennie

I can see some extensive Googling is required. And I was going to work this morning. Damn! :-)

ACuriousMind

The situation may be confusing because the FBI is both an intelligence service and a more federal law enforcement agency

Whereas in most other countries, these two things are split

The Raiders of Las Vegas

Who did 007 work for?

ACuriousMind

Or, well, I dunno about most, but at least in Germany and the UK

@TheRaidersofLasVegas MI6

The Raiders of Las Vegas

9:17 AM

Her Majesties Secret Service?

John Rennie

That most reliable of sources, the Internet, tells me the British equivalent of the FBI is the National Crime Agency.

The Raiders of Las Vegas

What's the KGB equivalent?

AccidentalFourierTransform

KFC

ACuriousMind

@JohnRennie I guess the question is now whether your thoughts are more likely to interest the NCA or the MI5 :P

I.e. are you just a criminal or do you have higher aspirations?

(I'm totally not a secret agent, by the way)

AccidentalFourierTransform

sure ¬¬

The Raiders of Las Vegas

9:21 AM

>.>

<.<

> ::checks VPN::

ACuriousMind

@AccidentalFourierTransform You can trust me.

John Rennie

@ACuriousMind some of my cooking probably counts as acts of terrorism ...

Maybe even crimes against humanity :-)

ACuriousMind

@JohnRennie Not any that you've posted here! Unless raising the incidence of heart disease counts...

The Raiders of Las Vegas

...weapons of mass destruction!

btw, not everything that counts, can be counted :P

ACuriousMind

True, water is an uncountable noun and still pretty important.

AccidentalFourierTransform

9:28 AM

Jun 7 at 17:03, by AccidentalFourierTransform

The Count Censored

►

The Raiders of Las Vegas

thnx for using the censored version

ACuriousMind

It's pretty sad that the "count" pun doesn't work in other languages

He just gets a random nobility title

The Raiders of Las Vegas

Baron?

ACuriousMind

He's a Graf in German

The Raiders of Las Vegas

I see.

AccidentalFourierTransform

9:38 AM

$\{(x,f(x))\}$, thats typically uncountable...

The Raiders of Las Vegas

...does that count?

AccidentalFourierTransform

there has to be some pun with the c-word

can we use the c-word here?

in the UK sense at least

ACuriousMind

@AccidentalFourierTransform I'd prefer you don't

Danu

Coincidentally, I need to learn about the c-map!

AccidentalFourierTransform

> Dyckmanns

what is a CASK manifold?

The Raiders of Las Vegas

9:56 AM

101 Illustrated Analysis Bedtime Stories

CooperCape

even the internet hasn't heard of a CASK manifold.

AccidentalFourierTransform

^

Anonymous

11:55 AM

I'm looking for a detailed description of the construction of Peltier tiles. None of the websites I visited are detailed enough. Please let me know if any of you know any article or website which describes the construction of Peltier tiles.

0celóñe7

12:35 PM

@ACuriousMind I woke up to the sound of the dog throwing up on me

2

that's why I prefer the cat

0celóñe7

1:15 PM

@BalarkaSen you here?

ACuriousMind

@0celóñe7 heh

Anonymous

2:39 PM

@ACuriousMind I have a QM question =P Under what conditions can the wave function (in Schrodinger's eqn.) $\psi(x,t)$ be written as $\psi(x)\phi(t)$ ? In my book they just took it as an assumption :/

Anonymous

I mean under what conditions can we separate the position dependent part and the time dependent part

Anonymous

It seems JR is not around.....:P

0celóñe7

@Blue That is a common technique for solving partial differential equations

Which would be clear to you if you learned this stuff in the right order...

But you may always write that if the initial data is an eigenfunction of the Hamiltonian.

ACuriousMind

@Blue If and only if it is an energy eigenstate aka "stationary state"

Anonymous

@ACuriousMind Okay, but why? Do you know any book or article which explains this?

0celóñe7

2:48 PM

@Blue Prove it yourself

ACuriousMind

@Blue Why what, exactly?

0celóñe7

@ACuriousMind Why did it take the walkers 5.8 seasons to do anything at all and why is this now a zombie movie?

ACuriousMind

@0celóñe7 Well, they were...walking.

0celóñe7

@Blue If you need a book, look up "Applied Partial Differential Equations" by Haberman

@ACuriousMind the walkers have horses and the dead can run at break neck speed

do we get any character development on the walkers at all?

ACuriousMind

@0celóñe7 You don't need a differential equations book to do QM with the Schrödinger equation :P

Anonymous

2:55 PM

@ACuriousMind Why can we separate the position dependent and time dependent parts iff it is an energy eigenfunction ?

ACuriousMind

@0celóñe7 So far, I'm not sure they have anything that qualifies as "character"

0celóñe7

@ACuriousMind anything that explain who they are/where they came from/motivations/etc.?

ACuriousMind

@Blue Well, what does it mean to be an energy eigenstate?

0celóñe7

Preferably from the guy with the crown

ACuriousMind

@0celóñe7 nope

CooperCape

2:59 PM

Is this the walking dead or something? Cause I'm seeing the words 'walkers' and 'slow' which is basically a plot summary.

0celóñe7

No, game of thrones

CooperCape

oh right

think i'm on season 5 but mehh.

glad to know the walkers have a function

0celóñe7

@ACuriousMind Are you sure what you said is true for time-dependent Hamiltonians?

ACuriousMind

@0celóñe7 No, time-dependent Hamiltonians are a plague to be avoided :P

0celóñe7

Ah, well.

@Blue Did you download the book I suggested

Sir Cumference

3:03 PM

Morning

0celóñe7

What ACM and I are telling you to do is called "separation of variables" and you won't dream it up on your own.

CooperCape

good website that explains seperation of variaables :webpages.ursinus.edu/lriley/courses/p212/lectures/node35.html

with schro-schros equation

ACuriousMind

@0celóñe7 Actually, I didn't want to tell him about separation of variables :P

The question wasn't why we do separation of variables or why it works, but which sort of state the separated states are

0celóñe7

And to prove that a separated state is stationary you need to apply the technique of separation of variables.

$H\psi/\psi=C_1$ and $\phi_t/\phi=C_2$

Anonymous

@ACuriousMind Say we've got $\hat{H}\psi=E\psi$ then for certain values of $E$ we get a legit value of $\psi$. The $E$ the energy eigenvalue...I hope I'm speaking sense...

0celóñe7

3:07 PM

What

CR Drost

That's a valid definition of an eigenfunction, yeah.

ACuriousMind

@0celóñe7 Huh? $U(t)\psi(x,0) = \psi(x,t) = f(t)\psi(x,0)$ (if my initial condition is at $t=0$) directly implies a separated state is an eigenstate of time evolution and hence of energy.

0celóñe7

@CRDrost How is "legit value of $\psi$" a valid anything?

CR Drost

Take the sentence as self-contained; "for most values of E that equation is garbage because it's unsolvable, but for some special values of E we can legitimately assign a value to psi."

Anonymous

@0celóñe7 I found the pdf. Can't read it right away. It'll take time. I'm trying to understand it now if possible. Or else I'll keep it in store for later when I complete PDEs

0celóñe7

3:11 PM

@CRDrost I legitmately do not understand what assigning value to $\psi$ is supposed to mean

Anonymous

We solve for $\psi$....as it is a differential equation....

CR Drost

@Blue: So getting the positions out of this... a function is very much like a vector, in that a vector takes an index n and assigns a component v_n. Now if you wanted to solve the equation dv/dt = M . v where M is a matrix, the easiest way to solve this is to diagonalize M. Then for these certain directions specified by the "eigenvectors", this equation is just dv/dt = \lambda v.

So you can now solve that very easily, v(t) = e^{\lambda t}~v(0).

0celóñe7

@ACuriousMind Blue does not know what $U(t)$ is. Do you not see my argument?

It's basic separation of variables. I know I'm a PDE guy, but c'mon.

ACuriousMind

@Blue That could be phrased better, but it will do. So now look at what I wrote above: $\exp(\mathrm{i}Ht)\psi = \psi(t) = \phi(t)\psi$ by assumption (I dropped the $x$ dependency because it doesn't matter), so $\psi$ is an eigenstate of the time evolution operator $\exp(\mathrm{i}Ht)$ for all $t$ with eigenvalue $\phi(t)$, and therefore also of $H$ itself.

CR Drost

@Blue Then the general solution requires a superposition of these, you start with v = \sum_i c_i v_i where v_i is an eigenvector with eigenvalue \lambda_i, this must evolve according to v = \sum_i c_i e^{\lambda_i t} v_i.

ACuriousMind

3:14 PM

@0celóñe7 Oh dear, are we doing Schrödinger equation before QM postulates here?

0celóñe7

@ACuriousMind I'm 99% sure we are.

ACuriousMind

Then I might have been barking up the wrong tree. I just can't into doing "QM" that way

0celóñe7

Which is why I gave my simple mathematical argument!

CR Drost

@Blue something similar happens as we generalize v_n to something like psi(x), in general one cannot separate psi(x, t) = psi(x) phi(t), but since the Hamiltonian is Hermitian it can be "diagonalized" in a basis of eigenfunctions, and in that basis the Schrodinger equation is very easy to solve.

0celóñe7

If you accept the axiom of physics math

CR Drost

3:18 PM

@Blue the actual mathematical theorem that one can diagonalize the Hamiltonian is called the "Spectral theorem", see en.wikipedia.org/wiki/Self-adjoint_operator#Spectral_theorem for example.

As 0celóñe7 is telling you the more general case is that you have a linear homogeneous partial differential equation D f = 0, seeing that D (f + g) = D f + D g, one thinks "well, let's assume that f = A(a) B(b) C(c)... for all of the independent variables a,b,c that we're taking partial derivatives of, and trust that this summation will get us all of the other solutions: what relationship do we find between the functions A, B, C?".

Usually one gets a really slick solution when one looks at Df / f = 0

So e.g. for the 1D heat equation {\partial f \over \partial t} - k {\partial^2 f \over \partial x^2} = 0, one assumes f = X(x) T(t) with the trust that after summation one will get the other solutions, D f / f = 0 gives us T'(t) - k X''(x) = 0, and the argument is that the left hand side cannot vary with either t or x because the right hand side doesn't, so T'(t) = \alpha and X''(x) = \beta and we have \alpha - k \beta = 0. We now have two ordinary differential equations.

That's called "separation of variables".

Whoops, sorry. T'(t)/T(t) - k X''(x)/X(x) = 0, that's super important.

Result is T'(t) = \alpha T(t) and X''(x) = \beta X(x) with \alpha - k \beta = 0 still.

Anonymous

@CRDrost I think I get it. The Hamiltonian is Hermitian...that helps. physicsforums.com/threads/…

Anonymous

Ok, I'll try to look at 0celo's argument too

0celóñe7

3:35 PM

@ACuriousMind Wait, what?

ACuriousMind

@0celóñe7 what wait?

@CRDrost FYI, you can use MathJax in chat as in posts on the site if you pick one of the ways to activate it for you first from the link in the room description in the upper right corner.

CR Drost

v cool

0celóñe7

@ACuriousMind You need some form of Stone's theorem for your argument. How could it possibly be simpler than mine?

John Rennie

Look on my works, ye Mighty, and despair!

0celóñe7

What happened to "I eat veg during the week"

John Rennie

3:49 PM

There's onion in the muffins (along with ham and cheese :-). Onions are veg.

0celóñe7

@JohnRennie Do onions have any nutritional value?

John Rennie

@0celóñe7 Actually I don't know. I would guess onions and garlic are pretty similar from a nutritional point of view. However they both taste good :-)

There aren't many calories in onion (or garlic) but I wouldn't advise making them the basis of a diet.

Anonymous

Onions and garlic taste good? whaaaaaaatttttttttttt!

Anonymous

I can't tolerate either

John Rennie

Heretic! Burn him!

0celóñe7

3:53 PM

Yeah, wtf @Blue

@JohnRennie I had cheeseburgers last night and put a half onion on each

It's a good plant