The h Bar

4:01 PM

I made G = 1 / 60

and that helped

Anonymous

If $\psi(x,t)$ (in Schrodinger's equation) is written as $\phi(x)T(t)$, then what is the physical significance of $T(t)$ which comes out to be $e^{\frac{-iEt}{\hbar}}$ ? If there were no imaginary term involved I could have thought of it as representing the time-evolution of $\phi(x)$. But then, we can write $e^{iz}=\cos(z)+i\sin(z)$. Does the imaginary part of $T(t)$ represent the time evolution of the imaginary part of $\phi$ ? Or something else?

ACuriousMind

@Blue it's the time evolution. What has it being complex to do with anything?

John Rennie

@Tobi Try modelling a circular orbit i.e. start with a tangential velocity $\sqrt(GM/r}$. My guess is that you'll find your orbit spirals outwards or inwards because your algorithm doesn't conserve energy.

Tobi

i did that, let me show you

Anonymous

@ACuriousMind Time evolution of "what" exactly. I think of a wave function's real part being a vibration/wave in the vertical plane (say) while I think of the wave function's imaginary part as the vibration/wave in the horizontal plane. $T(t)$ represents the time evolution of both the vertical and horizontal displacements?

Anonymous

4:05 PM

Aug 5 at 14:11, by AccidentalFourierTransform

real part=vertical displacement; imaginary part=horizontal displacement?

Tobi

gyazo.com/f31c7b28afaf8192e68c0d8a0555c46f

ACuriousMind

@Blue Displacement of what? It's a QM wavefunction, not an actual wave.

Do not think of a QM wavefunction as representing any sort of "vibration"

Anonymous

@ACuriousMind Matter waves?

Anonymous

@ACuriousMind uh

Anonymous

I think I'm thinking of wavefunctions the wrong way :/

0celóñe7

4:07 PM

@JohnRennie PC made it into the new apartment in one piece

ACuriousMind

@Blue Yes, it's a wavefunction that represents matter, but the only significance it really has is that its squared modulus gives the probability density to detect the particle at a given location

0celóñe7

Gonna have a pretty sweet setup

Going to Best Buy later. Good chance I'll have a new keyboard

ACuriousMind

$\psi(x)$ itself has no direct physical significance - it's not something "vibrating"

John Rennie

@Tobi it's hard to tell with an elliptical orbit, though at a glance that doesn't seem too bad. It doesn't obviously precess or change the maximum and minimum distances.

@0celóñe7 Cool :-) You back at university?

Anonymous

@ACuriousMind Ah. So we can't visulize it or simulate that wavefunction $\psi(x)$. I see. Difficult to digest it though

Prathyush Poduval

4:08 PM

@Blue Now if it were a single wave function, the phase term would drop out. But if there were a superposition of different wavefunctions, then the T term comes in the probability

ACuriousMind

@Blue Why wouldn't we be able to simulate it?

Prathyush Poduval

@Blue You can plot the probabilities, $|\psi|^2$ (remember what you did in jee qm :P?)

John Rennie

@Tobi you might want to Google runge katta orbit or something like that. The Runge Katta method is not a symplectic integrator but it's fairly simple and quite accurate.

Anonymous

@ACuriousMind By "simulate" I meant making a computer model of it. Like we can plot $A\sin(wt-kx)$ as a plane progressive wave on Desmos :P

Anonymous

Is there any similar way to "plot" $\psi(x,t)$ ? I hope not

John Rennie

4:10 PM

in The Nineteenth Byte, 1 min ago, by user3200293

"In the game of golf, you win by minimising the number of strokes to complete the game. "

Now where I'm from we call that a game of non-reproductive sex, not golf.

Anonymous

@PrathyushPoduval Yeah, but that's not what I'm asking

John Rennie

Some spoilsport just flagged that :-)

ACuriousMind

@Blue Well, you can plot a wavefunction, too. It's a function, you can plot functions regardless of whether they have any physical meaning

Prathyush Poduval

@Blue Well, you can imagine it as a vector if you want to

Tobi

what's wrong with velocity += M/r^2

Prathyush Poduval

4:12 PM

The sum of all the different vectors is a superposition

and the length os the vector is the probaility

ACuriousMind

@Tobi That you're treating the acceleration as constant over the duration of the frame when it isn't.

0celóñe7

@JohnRennie mhm

John Rennie

@Tobi you are assuming the acceleration is constant but of course it isn't. That means you over or under estimate the real velocity change.

Prathyush Poduval

@Blue people.fas.harvard.edu/~djmorin/waves/interference.pdf He deals with complex functions, and shows it geometrically, could be helpful

Tobi

what if i average it?

Prathyush Poduval

4:13 PM

go to the diffraction part

Tobi

of somehow find average

with like integration

or some maths

ACuriousMind

John already told you the correct solution, it's called a symplectic integrator.

Anonymous

@ACuriousMind Ok. So we can write $Ae^{i(kx)}.e^{-\frac{iEt}{\hbar}}$ and plot it to get the time evolution of horizontal and vertical displacements even though that has no physical significance. I get it. Thanks

ACuriousMind

@Blue ...why is there both an $\omega t$ and an $Et$ term in there?

John Rennie

@Tobi I have done that in the past and it does help. Take a at your start point and calculate the end point, then calculate a at the end point. Now average the two values of a, then go back to your start point and recalculate the velocity change. Repeat this until the value of a converges.

The only problem is that this isn't a very efficient algorithm.

Anonymous

4:15 PM

@ACuriousMind Oops...typo

John Rennie

@ACuriousMind to be fair symplectic integrators are not beginner friendly ...

Tobi

can't I use integration/differentiation, as opposed to brute force

John Rennie

Well you are using integration. You are performing a numerical integration of the equation of motion.

You can calculate the trajectory analytically by solving the equation of motion, but that's surprisingly painful for orbital motion.

Anonymous

@PrathyushPoduval Ah, I was looking for the "physical significance" of the $T(t)$ separately I guess. But thanks. I look through it

Anonymous

As ACM said, $\psi$ doesn't have any physical significance by itself

Anonymous

4:18 PM

I think I get it

Tobi

im confused again

i havent been to university

only a level physics

0celóñe7

@ACuriousMind what?

Tobi

if i plot a graph of a / t, the area under graph is change in velocity, correct?

I could integrate the equation relating acceleration and time

between two intervals

0celóñe7

I've never heard of that

Prathyush Poduval

@Blue Yes there is no significance. But, the vector analogy has gotten me thinking now......

Anonymous

4:22 PM

Vector analogy is just to make the math easy...I don't think it contributes much to the logic.

Tobi

connected rates of change!!!!

a-r r-v v-t

John Rennie

@Tobi yes, but unless you can do the integration analytically you typically calculate the area by using small strips of some width $\Delta t$.

Tobi

can't you find exact forumla

instead of strips

i.e: area under 2x = x^2

instead of using strips under graph

John Rennie

Yes, for orbits you can solve the equation analytically and get a precise formula for the position and speed as a function of time. But the equations are pretty complicated.

Tobi

complicated to a human

Prathyush Poduval

4:26 PM

@Blue Just because something doesn't contribute much doesn't mean it's not worth taking a look into it :P

Tobi

they're single expressions for a computer, as opposed to a function involving segmenting graph

John Rennie

@Tobi I think you're talking about symbolic integration but that's pretty hard.

Programs like Mathematica and Matlab can do it, but thoise are big and expensive apps.

Tobi

what are you talking about? i thought that was normal integration

John Rennie

Yes, but you're asking the computer to do it aren't you?

Tobi

i can figure out the formula on paper, and hardcode it

Anonymous

4:29 PM

@PrathyushPoduval I never said that. I'll take a look at it. (I think I did read that article you linked sometime earlier...in grade 12)

Anonymous

Thanks though :)

John Rennie

@Tobi Ah OK, we are talking at cross purposes. Yes, you can do the integration yourself on paper. But for orbits involving only two bodies it's complicated and for three or more bodies you can't do it at all.

ACuriousMind

@0celóñe7 Well, have you dealt with numerical solutions of differential equations to simulate physical systems?

Tobi

the change in velocities are individual

you run the formula for each pair

ACuriousMind

@JohnRennie Indeed they aren't, but as far as I know there's no better solution to the "not conserving energy" problem

John Rennie

4:32 PM

@ACuriousMind Runge Katta is pretty good and fairly simple to implement

ACuriousMind

@Tobi Of course you can, but then you're not doing what one would call a "simulation", you're just plotting analytical results

Tobi

what do you mean

John Rennie

I suspect we are talking at cross purposes again.

Tobi

for each interval, you grab each pair ( O(n^2) ) and calc change in velocity, due to gravity

what do you mean by cross purpose?

John Rennie

@Tobi I mean we are taking about different things

ACuriousMind

4:34 PM

Also, as soon as you have more than two objects, you can't hardcode the analytical solution anymore because the n-body problem doesn't have a general analytical solution

Tobi

what im doing is updating velocity at regular intervals

if you have 3 objects, you run the gravity change on every object twice

so it accounts for every other gravitational field

John Rennie

@Tobi but your calculated change in velocity is an approximation

Tobi

how so?

lemme show you what i mean

John Rennie

Because when more than 2 bodies are involved there is no equation that exactly describes the velocity change

Tobi

prntscr.com/g99m4g

John Rennie

4:37 PM

Yes you can calculate the acceleration at a moment in time. But as soon as your objects move the acceleration changes.

Tobi

hence integration of a/t, for delta v

John Rennie

So if you assume a constant acceleration for some small time $\Delta t$ and use that to calculate the motion your calculated motion will be wrong.

And when three bodies are present there is no equation to calculate exactly how the acceleration changes with time

dmckee

@ACuriousMind It's poorly worded. The text reads like it is identifying a particular so—this one electron decayed after 80ns—so the reader has to infer that this is a typical lifetime before they can even begin.

Or take a Baysean stance that the one observation represent their best current knowledge.

But either way that is a unecessary sticking point.

Tobi

@JohnRennie you use the resultant vector, of the change in velocity, calcuated via integration, not constant acceleration

John Rennie

When three bodies are present you can't do the integration

dmckee

4:40 PM

Certainly the physics connection between lifetimes and width is important.

ACuriousMind

@Tobi Point is you can't "calculate via integration" for more than two bodies.

John Rennie

Three-body problem

In physics and classical mechanics, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses, and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with Newton's laws of motion and of universal gravitation which are the laws of classical mechanics. The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth, and the Sun. In an extended modern sense...

Tobi

maybe i just solved a physics problem

cos it makes sense in my head

John Rennie

Then you should write to the Nobel committee immediately

Tobi

Isn't that a bit arrogant

is ur proposal to use smaller time intervals

John Rennie

4:43 PM

My proposal is that you should use a more sophisticated way of calculating the motion. The Runge Katta method is good and still reasonably simple.

Symplectic integration is best, but there is some scary maths involved - I would hesitate before attempting to implement a symplectic integrator.

0celóñe7

What the hell are you people talking about

@ACuriousMind yes

ACuriousMind

then you should know what the hell we are talking about :P

Tobi

i hate physics

ACuriousMind

What are you doing in a physics chat, then? :P

0celóñe7

@ACuriousMind I just do RK and put the step size small

I have a good COU

@Tobi good man

Anonymous

4:54 PM

@ACuriousMind Even @0celóñe7 hates physics but yet he lives here :P

0celóñe7

Because I love the people here

Anonymous

This chat is for both who love physics and hate physics. Not for those who don't care about it :D

0celóñe7

@ACuriousMind is forgetting that stack exchange is a social network

Anonymous

@0celóñe7 awww :'D

ACuriousMind

@Blue His superficial hatred is but a mask for a deep-seated love.

0celóñe7

4:56 PM

I won't deny a love for parts of physics

Tobi

how can you love it

its unnecessary brain strain

0celóñe7

Are you a mathematician?

Prathyush Poduval

5:12 PM

@Blue Oh sorry, i must have misunderstood then. I never though of the wave function having any physical meaning, and your questions got me thinking

John Rennie

@Tobi if physics were easy it wouldn't be a challenge and there wouldn't be any sense of satisfaction when you finally understood some part of it.

Tobi

@0celóñe7 nope, CS

Anonymous

@PrathyushPoduval What does Feynman say about that? (Did you read his lectures on that topic?)

Tobi

@JohnRennie everything was solved 100 years ago

todays physicists are theorists

Anonymous

lol.

Secret

5:15 PM

not really, wait until you touch astronomy and condensed matter

you will found out how deep this rabbit hole is

John Rennie

Or quantum optics. That's a scary deep rabbit hole :-)

Prathyush Poduval

@Blue Nope, i didn't read his book on it. I got bored when I read it, since he went on about electron beams and all. I prefer a (somewhat rigorous) mathematical treatment on the topic (a.k.a Griffiths :P)

dmckee

@Tobi ::facepalm::

Anonymous

In physics most often experiments help to point out faults in theory. And then the theory is modified (or atleast people try to do so).

0celóñe7

@dmckee you god damn theorist

@Tobi has spoken

Anonymous

5:19 PM

@PrathyushPoduval An interesting set of comments (researchgate.net/post/…)

2

dmckee

Classroom physics is mostly theory, and the physics in poop-sci books is mostly theory.

Secret

pooooooooooooooooooooooooooooooooop-sci book

dmckee

But physics in the real world is complicated, messy, and very much bothered with the real wolrd.

Prathyush Poduval

@Blue Most of them are saying "no,no,no....":P

dmckee

@Secret ::chuchles:: I've made that typo twice recently. A Freudian would say my subconscious is trying to tell me something.

Prathyush Poduval

5:21 PM

But i found this link journals.aps.org/pra/abstract/10.1103/PhysRevA.47.4616 there

2

Anonymous

@PrathyushPoduval Check Malcolm White's comment

Secret

well, they are quite terrible at communicate the more abstract experimental results accurately like quantum weirdness and particle physics stuff

but then, it is practically impossible to teach high level group theory to a toddler

Prathyush Poduval

@Blue That does make a lot of sense

Your asking for the physical meaning of something which describe our notion of "physicsal meaning"

dmckee

Quantum fundamentals is where physics careers go to die.

2

Which is funny because we're all interested in the subject. But smart people do it after tenure or as a retirement project.

Anonymous

Quantum computing seems to be a career path with lot of scope though.

dmckee

5:25 PM

And it will doubtless throw much fuel on the fire of quantum fundamentals.

We should be making popcorn or something.

vzn

@dmckee (lol) and do you think Bell or Bohm had careers that "died"?

@PrathyushPoduval try eg Cavalcanti/ Fedrizzi (et al) for more recent ideas newscientist.com/article/…

Prathyush Poduval

@vzn Thanks, going through it

Secret

Everybody in physics seemed to be looking forward to larger commericial quantum computers by the end of this year, as far rumors has it

Tobi

If two objects are receding

Secret

and we computational chemist too, for an enzyme reaction pathways can be speed up to take just minutes to done on a quanutm computer

Tobi

5:34 PM

will they eventually meet, due to gravity

vzn

@PrathyushPoduval so what are your thoughts then?

Prathyush Poduval

@vzn Well, I dont contest the fact that the wave function is real

It was just, whether you can get some physical meaning of it

vzn

@PrathyushPoduval huh, freudian slip? you seem to have phrased that incorrectly?

Secret

For me, I am psi ontic and agnostic on the interaction that lead to measurement, but I am perfectly fine working with psi epistemic models if need to. I am also learning some Qbism

Prathyush Poduval

@vzn Nope :P, its like how wave function(not QM) gives you the position of particles vectors give you the displacement of the particles.

So when blue asked the question whether it had any physical meaning, I thought about the wave function being imagined as a rotating vector in 2d

vzn

5:38 PM

@PrathyushPoduval the copenhagen interpretation seems to inherently deny the "reality of the wavefn". are you a student? physics? india?

@PrathyushPoduval a very worthwhile/ substantial/ significant question! have some (new) ideas along those lines if you want to hear them. :)

Prathyush Poduval

@vzn Oh no, I t was just an idea, nothing serious

@vzn I would very much like to

Secret

no, cophenhagan is agnostic of the reality of the wavefunction, it neither denies nor embrace it

vzn

@PrathyushPoduval ok, am working out details, but there are (many) other physical/ classical waves that can be represented with complex fns. unf this is rarely taught or emphasized.

Prathyush Poduval

@vzn The thing is, I saw a similar thing in optics

Anonymous

@PrathyushPoduval By optics you probably mean wave optics(?)

Prathyush Poduval

5:40 PM

@Blue yup

The handout i sent you

@vzn people.fas.harvard.edu/~djmorin/waves/interference.pdf this is where i saw it

vzn

speaking earlier of rabbit holes, personally think the ultimate rabbit hole is reinterpretation of QM wrt reality of wavefn etc...

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