The h Bar

Let $A$ be some observable. Then
$\sum_{i=1}^{n}A_{ii}^e \equiv \sum_{i=1}^{n}\langle e_i | A | e_i \rangle$ is the expectation value of A, but $\langle e_i | A | e_j \rangle$, does not have physical interpretation on its own (I forgot whether $(\langle e_i | A | e_j \rangle)^2$ have physical meaning for generic A, either, though if that is H, then that expression will be the probability of the state $e_i$ becomeing $e_j$ )

Anonymous

@BalarkaSen It's in the second semester. Before that I have to learn Complex Analysis, Real Analysis, Vector Calculus, advanced Differential Calculus and Differential Equations in first semester. I'm short of time. Moreover here the prof directly jumped to Schrodinger's equation without teaching QM and linear algebra

user400188

@Secret Isn't it true, that part of the definition of an observable is "some physically measurable quantity" ?

Balarka Sen

@Blue Not good. Linear algebra should come before alll of that

user400188

Would it not be the case then, that it has a physical interpretation by definition?

Anonymous

8:20 AM

@BalarkaSen Yeah ;-;

Anonymous

I'm trying to pick up as much I can on the way

user400188

@Secret Oh never mind... The expectation value of $A$ is not $A$ itself.

Secret

Sure, but you will need to enclose it in bra-kets in order to extract the meaing from it. If the state $\lvert \psi\rangle$being act on by the operator is not an eigenstate of A, then $A\lvert \psi\rangle$ has no physical meaning

Balarka Sen

Ted's lectures are a good course on linear algebra

I can give you a crash course on the part of linear algebra you need to know

Anonymous

@BalarkaSen how?

user400188

8:23 AM

@Secret Ah, i see what you mean now

Secret

Matrix elements also don't have physical meaning on its own until you mod square it

Balarka Sen

@Blue By telling you a bunch of stuff in a separate chat from hbar.

Secret

because anything that has physical meaning in quantum should not depend on how we pick the basis set

user400188

Interesting

Anonymous

@BalarkaSen Sure. When?

user400188

8:24 AM

@Secret Actualy, I have been wondering about that.. Does the wave function itself have a physical meaning?

or just its mod squared?

Balarka Sen

@Blue I need to get some of my schoolwork done. When is good for you? 7 PM today would be ideal for me

I can shift my time around if you want. I mostly don't care about schoolwork

Anonymous

@BalarkaSen I'm free. Today is a Sunday. How long would it take though? We can space it out over one week if you wish. Like 30 mins for 7 days :P

Balarka Sen

Fun idea. I'm down for that.

Anonymous

"down" or "up" ?

Anonymous

:P

Secret

8:27 AM

That is still not fully settled as far I know given the amount of interpretations out there. In cophenhagen interpretation, we don't ascribe physical meaning to the wavefunction. In instrumentalist view, we don't even care about the wavefunction. In psi-epistemic interpretations, the wavefunction is just a summary of the knowledge we know about the quantum system and not really a physical thing. Only in psi-ontic interpretations, do the wavefunction is a physical entity associated with the

2

quantum state

Balarka Sen

all directions lead to rome

Anonymous

@BalarkaSen :)...okay, if you are free from 7-7:30 we can do it. Just ping me once...i should be online

Secret

as far I know and remember, the latest experiments only suggests some psi-epistemic models are not very compatible with what happens in experiments, but it seems to be still an open question whether the wavefunction is a physical property of the quantum system

Balarka Sen

@Blue K

Anonymous

Maybe we can follow the sequence of topics given here

Secret

8:31 AM

But for issues related to interpretations, Emilo Pisanty, Acuriousmind and Danielsank will be a better person to ask

user400188

Thanks for the referal @Secret (and the answer)

Balarka Sen

@Blue Let's see what we'll do

Secret

O almost forgot, the wavefunction is also a physical thing in nonlocal hidden variable theories such as Bohmian mechanics, where it is a pilot wave that guide the trajectory of the particles, however this is not a very popular model as it has problems with going relativistic

Anonymous

@JohnRennie For electrons can we write the $V(r)$ function as just $\frac{k(Ze)}{r}$ ? But that seems wrong when inter-atomic interactions are present. Also how do we write the potential function for free electrons?

John Rennie

@Blue That's the potential for an electron in an isolated single electron atom with charge $Z$ ...

Anonymous

8:41 AM

I wanted to know how to find the $V(x)$ in $\hat{H}$ for electrons

John Rennie

It's simpler than you think. It's normally just the classical PE.

A free electron has $V=0$

Anonymous

@JohnRennie So, isn't that the $V(r)$ ?

Anonymous

For a bounded electron

John Rennie

@Blue Yes

Anonymous

Oh. For free electrons V=0. I'm stupid =P

John Rennie

8:43 AM

:-)

Re all this QM stuff ...

Anonymous

@JohnRennie ?

John Rennie

Approaching the subject using linear algebra probably seems very abstract and you may wonder what it has to do with the real world.

Anonymous

Yeah...that's what I was wondering XD

John Rennie

The point of learning QM this way is that you get a real understanding of the mathematical foundations of the theory.

Then when you start on the really screwy stuff, like quantum optics, you'll have some idea what it's all about

You don't need the mathematical background if you want to do is hydrogen atoms

But that won't get you very far in modern physics :-)

Anonymous

@JohnRennie I want to do higher studies in areas like photonics or particle physics. So I'll definitely need to know the math. :P However, I don't like raw math without intuitively being able to relate it to the real world

Anonymous

8:47 AM

@JohnRennie yeah

Anonymous

hehe

John Rennie

@Blue I sympathise with your point of view because I feel the same. In fact back in the 80s when I first learned QM it was taught in the traditional way i.e. hydrogen atoms.

But the trouble is that as a result I really struggle to provide good answers on QM on this site. People like Daniel, or indeed any of the other serious QM heads, make me look like a beginner!

Anonymous

@JohnRennie I see. So you relearned it again later on? (with the math?)

Anonymous

How long does it take to properly understand QM ? (I mean atleast at the graduate level)

John Rennie

I've managed to partially relearn it, but it's an uphill struggle to forget everything you learned and relearn it properly :)

At least with GR I didn't know anything about it before joining this site so I didn't have any bad habits to try and forget.

Anonymous

8:50 AM

@JohnRennie Hehe. Well, Daniel has a PhD in quantum electronics =P

Avantgarde

@Blue As much time as you can take to solve Sakurai's book with an easier book on the side

John Rennie

I don't think it takes long to get a pretty good grasp of QM if you have a good teacher - a few months maybe.

Anonymous

@Avantgarde Sakurai is too hi-fi for me at the moment. I'm learning from Allan Adam's lectures. Our electronics prof just skipped over the basics. Anyway, hope to catch up soon.

Anonymous

@JohnRennie relief :)

Avantgarde

@Blue I've never been through his lectures. But you asked for grad level QM expertise ;)

John Rennie

8:55 AM

@Blue are you doing QM at college, or is this just out of personal curiousity?

Avantgarde

Shankar is pretty nice for a longer exposition and he explains various little details

Anonymous

@JohnRennie Check out the Physical Electronics part of this syllabus. It has some selected parts of QM but not all of it. I'm trying to learn QM in detail as I wish to pursue higher studies in physics after my B.E. For engineering we don't need to know so much. Just simple hydrogen atom model will do :P

Anonymous

I'm sure that most EE engineers don't understand QM well

Avantgarde

I think JU has a pretty nice physics department as well? Why don't you try and sit for the physics lectures there, if you can?

Anonymous

@Avantgarde I called up a physics professor. He asked me to meet him on Monday. Let's see. This guy-------> nbmanik.in

Anonymous

9:00 AM

Even if he doesn't allow me to audit lectures (due to time clash) maybe he'll take me into some projects

Anonymous

Hoping for the best

Avantgarde

Pretty nice. Do talk to him. He'll be happy to help you out, I hope.

Secret

9:17 AM

@Blue I have the opposite problem: Relatioal existence is being abused so much that I think I can use the maths to derive all the physics. As a result, I end up over interpreting the abstract as physical things which actually does not exist

Secret

0

Q: Are the frequencies of a photon real motions if so is this motion limited by the speed of light?

In Newtonian language a photon oscillates to get his frequency. In the quantum field theory the photon is an excitation of the electromagnetic field. But are these excitations also limited by the speed of light giving the frequency of a photon a maximum?

Hmm... is there a speed limit to the rate of change of the value of an electric field at a point in spacetime?

More generally, is there a limit to how large first derivatives in physical process can be?

It will be interesting if a change approach the orders of magnitude of the speed of light, it started to experience relatvistic effects

Secret

9:39 AM

6

A: What is the highest possible frequency for an EM wave?

It's theorized that the Planck length is the smallest meaningful unit of distance. A wave with that wavelength would have a frequency of $\approx 6.2\cdot 10^{34}\,\text{Hz}$. A gamma ray typically has a frequency of $>10^{19}\,\text{Hz}$. Since the energy of a photon is directly proportional to ...

39

Q: Are there any theoretical limits on the energy of a photon?

Is there any lower or upper limit on the energy of a photon? i.e. does the mathematical framework we currently use to study photons blow up when a photon surpasses a certain upper limit of energy? (or the same on the opposite side?) My thoughts: If I let the energy of a photon tend to infinity, ...

quantum-mechanics energy photons wavelength

cannot believe this is a QG question

Anonymous

Anonymous

What does "neutrino scattering" of electron mean?

Anonymous

@JohnRennie halp =P

Qmechanic

1

Q: How does the human ear guess the source of the sound?

Suppose a sound is produced behind you. You can easily tell that the sound came from behind. Our ear lobes face towards the front and hence traps the sound waves which come from the front. Yet, we can detect that the sound came from behind. We can claim that the sound which was produced behind t...

acoustics reflection biology perception

Off-topic?

Anonymous

Belongs to bio se probably

Anonymous

9:52 AM

Can't we migrate it?

Anonymous

@Yashas Man, we miss you :P

John Rennie

@Blue I think that's the 1973 observation of a neutrino scattering off an electron at the Gargamelle experiment.

It was a critical observation because it proved the existence of weak neutral currents.

And that was a key part of the Standard Model.

Anonymous

@JohnRennie You mean neutrinos were deflected by an electron and that proved the existence of "weak neutral currents"? What does "neutral current" mean btw?

Anonymous

Neutral current

Weak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the Z boson. The discovery of weak neutral currents was a significant step toward the unification of electromagnetism and the weak force into the electroweak force, and led to the discovery of the W and Z bosons. == In simple terms == The weak force is best known for its role in nuclear decay. It has very short range but (apart from gravity) is the only force to interact with electrons, neutrinos, and quarks. The weak force is communicated...

John Rennie

@Blue Yes. That Wikipedia article seems to cover weak neutral currents well ...

Anonymous

9:59 AM

I see. Interesting! :D

Anonymous

10:41 AM

All this time I thought that the wave model explains the YDSE experiment. Just got to know that even that doesn't work. An electron or photon can interfere with itself :O All the mathematical derivation of YDSE I was taught in school was wrong!

John Rennie

Welcome to the real world :-)

Anonymous

Seems everything I know is wrong :P

John Rennie

In the YDSE the particle (electron or photon) is delocalised so it doesn't have a position.

So it makes no sense to say the particle goes through one slit or the other.

Anonymous

@JohnRennie I still couldn't understand the interference "with itself" part...that should mean it goes through both of the slits

Anonymous

That too with a phase difference

John Rennie

10:45 AM

The particle is, to a good approximation, a plane wave i.e. a momentum eigenstate.

The diffraction is simply the evolution of the plane wave as it passes through both slits.

Anonymous

Can we think of it as ripples in a pond?

John Rennie

If you wish, though the particle isn't a ripple in anything.

Anonymous

@JohnRennie What do you mean by "evolution" ?

John Rennie

The way the wave changes as it moves through space

Anonymous

Ok. What about the interference ?

Anonymous

10:52 AM

Diffraction can be explained by wave model

John Rennie

Interference and diffraction are the same thing

Anonymous

Oh. Considering infinite number of tiny slits? Oh, yes

John Rennie

@Kaumudi.H you around?

Tobi

1

Q: Calculating circle rebound

I'm computational modelling circular collisions. I have the x-y components of the circles' velocity vectors (green lines) I'm trying to calculate the resultant rebound velocities When the collision is head-on, using conservation of momentum and energy, I calculated the formulas: $$ v_2 = \fra...

kinematics angular-momentum momentum velocity collision

user228700

@JohnRennie I am now! Hi! :-)

Anonymous

11:00 AM

Hi

user228700

Yello!

John Rennie

Hi. I saw your avatar appear but you normally say hello immediately so I wondered if you'd just left your PC on or something.

user228700

Ah, no, actually, I had been speaking with a senior! :-o He's working on Image processing using neural networks and machine learning.

Anonymous

@Kaumudi.H cool stuff

user228700

Seeking guidance etc. :-P

John Rennie

11:02 AM

You're back in Kochi?

user228700

Nope, still in Chennai; my bus is at 7:00 PM.

John Rennie

Gosh, Monday morning is going to be a struggle :-)

If you're interested I finally got around to trying chole with Maggi noodles ...

user228700

@JohnRennie It is! :-( I hope my bus reaches on time.

user228700

@JohnRennie OOH, what did you make?

John Rennie

It doesn't look all that great but it tasted really good :-)

user228700

11:05 AM

Chole?! :-)

John Rennie

I took some chole then added cream to it. That made the sauce.

Then I prepared the noodles, strained off the water and stirred the chole and cream into the noodles.

Anonymous

Chole isn't especially tasty unless you have some good gravy or sauce to go with it

user228700

@JohnRennie OOOH, nice! :-D

Anonymous

@JohnRennie What cream? cheese?

John Rennie

@Blue maybe what is described as chole in the UK is a bit different to what you're used to. Here it's chick peas in a spicy sauce, so it's very tasty.

@Blue cream as in the cream you get from milk.

Fresh cream

Secret

11:09 AM

This is not helpful. Have been spending 3 days on this:

Anonymous

@JohnRennie Ooooo....so the sauce makes it tasty :)

Secret

effbot.org/zone/default-values.htm

John Rennie

Yes

Secret

def myfunc(value=None):
if value is None:
value = []
# modify value here

John Rennie

I was going to sprinkle chopped fresh chillis on the top, but I forgot to buy any :-)

Secret

11:10 AM

Why doing it that way the default value will be left untouched despite sharing the same name as "value"?

Anonymous

Probably it's a problem with the scope of the variable

Anonymous

In java there is a "this" keyword to overcome that problem

John Rennie

@Secret the point of the code is to make sure that myfunc() returns the same every time it's called

The first time you call myfunc() value gets set to whatever, but the second time because value is no longer None it doesn't get changed.

Secret

Hmm... let's see if I understood you correctly...:

Using this:

def f(a, L=None):
if L is None:
L = []
L.append(a)
return L

So... on my first call of f(1), ....

L is set to None. Since it is None it then get set to [], 1 is tend appended to L to give [1]

John Rennie

Yes

Secret

11:21 AM

On my second call of f(1), L is [1] thus no longer None, thus it is not changed, but then L will be [1] and I will get [1,1]?

(NB: Sorry that chat removed the indent, but the only indent that followed the if statement is L =[])

John Rennie

I can't see how you've indented the code because the indents have been lost

@Secret In that case the line L.append(a) will get executed and the function will return [1,1]

Hmm, even using fixed font the leading spaces get swallowed ...

Secret

https://docs.python.org/2/tutorial/controlflow.html
See the section "If you don’t want the default to be shared between subsequent calls, you can write the function like this instead:" for the code

It looks like this. Somehow the L does not get appended endlessly

John Rennie

Ah, OK, I think I see.

The default value gets stored in some bit of memory, and that bit of memory is only initialised once.

The first code snippet initialises that bit of memory to [] and appending to this adds elements to the array

The second code snippet initualises the bit of memory to None and you can't append to None

So in the second snippet the line L = [] creates a new array that is distinct from the bit of memory where the default variable None is stored.

Secret

O wow, now I see, that's indeed quite confusing. so that means even though L=None and L = [] both use the same name L, they are actually referring to two different bits of memory

John Rennie

Yes, or at least I think so.

That certainly explains the observed behaviour.

Anonymous

11:35 AM

56

Q: What is a None value?

I have been studying Python, and I read a chapter which describes the None value, but unfortunately this book isn't very clear at some points. I thought that I would find the answer to my question, if I share it there. I want to know what the None value is and what do you use it for? And also, ...

python variables if-statement

Anonymous

That book isn't too helpful; None is not a default empty state for variables. — Martijn Pieters ♦ Oct 20 '13 at 2:11

Anonymous

Maybe that explains why L=None is different from L=[]

Anonymous

I need to learn python!

Secret

11:48 AM

Just found a nice answer that confirms Johnrennie's answer

-1

Q: default value for the function python

I'm trying to understand this question and answers: python function default parameter is evaluated only once? in order to understand it i try: def f1(a, L=[]): if not L: print "L is empty" L = [] L.append(a) return L >>>f1(1) L is empty [1] >>>f1(1) L is empty [1] ...

python

TWO F******* THINGS WITH THE SAME NAME!!!

(Should keep this two different bits of thing in mind when programming)

Yashas

12:12 PM

@Blue Toooooooo busy

@Qmechanic if the human ear has to identify the location, there must be something different with the sound itself... I was looking for that character of the sound which helps

heather

@DawoodibnKareem oh, thanks - should've noticed.

@vzn yeah, I've only got a couple weeks of summer left =/ i'll be taking algebra II, honors english I, spanish II, physical science (required), social studies (required), intro to engineering, and of course P.E./health

well, i guess technically english/algebra ii are required...whatever.

The Raiders of Las Vegas

algebra II is trig, right?

heather

nope, two separate classes

for us it goes alg I, geometry, alg II, trig, precalc, calc I, calc II, and then prob and stats somewhere in there.

that's if you take all math classes offered which are in the right 'track'

The Raiders of Las Vegas

12:28 PM

icic

seems a bit odd to isolate trig

that's 8 courses over 4 years?

of math

heather

yeah, but three of those years are block scheduling, so you can take two math classes in a year.

and i've already taken the first two classes.

and then there are a couple of courses you can take together - like trig and prob and stats at the same time.

0celóñe7

12:44 PM

@heather why are you up

ACuriousMind

ARCH ENEMY - We Will Rise (OFFICIAL VIDEO)

►

I'm back! (and pleased to see the place hasn't burned down)

Danu

Hey @ACuriousMind!

Where have you been?

heather

@0celóñe7 I got up early - I had my window open for the night and it was so nice out I couldn't bring myself to sleep late. also, it got really bright in my room. it's not that early either - 7:46.

i have to get up for school at 6:00.

Danu

@ACuriousMind God, is this the kind of music you listen to? :P

ACuriousMind

@Danu In Wacken

@Danu Yes, yes it is :D

Danu

12:47 PM

@ACuriousMind Hmm... :P

What was going on in Wacken?

0celóñe7

@ACuriousMind I think I sent you some vital @ messages

Danu

Oh, I see

0celóñe7

Also some messages about your death

ACuriousMind

@Danu The world's largest metal festival?

Danu

wacken.com

0celóñe7

12:48 PM

Which apparently did not happen

Danu

Party party

0celóñe7

@ACuriousMind most people have not heard of it

ACuriousMind

@0celóñe7 My inbox has like 30 items, about a third seem to be your pings

user685252

heavy metal is not as popular as it used to be

0celóñe7

@ACuriousMind good

I actually have no idea what they are for

Danu

12:52 PM

Any thoughts about your plans after the summer, @ACuriousMind?

Balarka Sen

hey @ACuriousMind

user685252

who knows, we could have another "golden age" of heavy metal

Balarka Sen

pls no

0celóñe7

@BalarkaSen No, it's a map from a dense subspace of $V$ to $V$.

ACuriousMind

@Danu not yet, introspective contemplation was very much not on the schedule last week ;)

Balarka Sen

12:59 PM

@0celóñe7 I see

Danu

:D fair enough

0celóñe7

@BalarkaSen There is no good way to extend $\Delta$ (Laplacian) to all of $L^2$. It's known that a symmetric operator defined on the entirety of a Hilbert space is bounded.

Balarka Sen

i never understand if the following for heavy slash death metal is for the complicated instrumental techniques they use or just because it's non-mainstream or ...

i mean let's agree that death growls are not melodic

not that i have anything against that shitz :p

user685252

it's an "acquired" taste

ACuriousMind

@BalarkaSen Not all metal is death metal, and not all death metal lacks clear vocals ;)

user685252

1:06 PM

cult-like in some ways

@BalarkaSen do some home work

Balarka Sen

@ACuriousMind you have to excuse my naivety there; i am not well versed in that realm. But all the good metals I have listened to have progressive elements in them, and are mostly instrumental.

0celóñe7

@ACuriousMind I am trying to position the cat next to the PC but it's not working

user685252

MIT Heavy Metal 101 is probably briefer @BalarkaSen

ACuriousMind

@0celóñe7 put a box next to it

Balarka Sen

Look what I found: youtube.com/watch?v=nKS1WTM6fzg

How come I did not know the existence of this???

0celóñe7

1:18 PM

@ACuriousMind He doesn't like boxes, and protested when I tried to put him in one