The h Bar

12:09 AM

nvm found the relevant section in the book

For an electromagnetic wave which propagates in some arbitrary direction and it's true that $k_z=\sqrt{k^2 - k_x^2 -k_y^2}$ is imaginary, it means that alongside the z axis, the wave doesn't propagate. Does this mean that we can have components of an electric field that propagate and can be mathematically represented with plane waves, and components that are evanescent waves?

Obliv

12:22 AM

wait does that work lol

that's so cool :P

seems like yes? @imbaf

Sir Cumference

12:56 AM

I'm genuinely surprised Sakurai doesn't bother to derive the Dyson series

Seems bizarre since it's got an honestly cool derivation in other books

Well this technically is a derivation, but it feels like a speedrun

ACuriousMind

Dyson series any%

2

Obliv

what book is that one

Sir Cumference

the picture? Sakurai

tbh sakurai started out really good but has been kinda declining in quality lately

guess he got tired of deriving a lot of things and just said to look at other books

Obliv

ohh I see what u mean

Sir Cumference

wish he didn't point to Townsend though

Obliv

1:10 AM

I feel like the point of a textbook is to guide the reader and deriving results plays a pretty big role lol

I'd say it's essential. If you're not going to bother doing that then don't write a book. The exception is if the derivation is just tedious but not difficult, or if it's just a copy/paste of a previous derivation with slight modifications.

Sir Cumference

well there are sections in this book that just really drag on because he goes into every detail on the derivation

which gets surprisingly boring

but then conversely there are sections where he just drops things out of thin air and says to read other books for the derivation

it's pretty much one extreme or the other

Obliv

I don't mind it if the author explains the gist of the result & how it's derived. Schroeder is so laid back in that way which I appreciate. Not that the derivations are actually that hard (I guess they can be, depending on how rigorous you want to be)

but stat mech/thermo is a lot easier to comprehend since it's not as abstract as QM

shrug

Sir Cumference

well it kind of depends

schroeder made statmech very intuitive for me

but then my graduate textbook made it feel incredibly difficult

so I've had a much easier time with graduate QM

it really comes down to whether you get a decent book at the end of the day. which is up to luck given that the prof chooses them

Obliv

@SirCumference in what way

Sir Cumference

@Obliv Sakurai honestly does a very good job connecting QM to (higher level) classical mechanics

Obliv

1:18 AM

yeah I guess it depends on the book and course. Any subject can get absurdly difficult :P

Sir Cumference

at the end of the day it almost feels like a modification of familiar things rather than a completely new topic

Obliv

what did u use for undergrad QM

Sir Cumference

Townsend (garbage)

Obliv

@SirCumference yeah that's ideally how it is.

Sir Cumference

that book is ass. just dropped the topic out of thin air and made every result seem arbitrary

sakurai is far better on the whole

Obliv

1:20 AM

ok well I hope we don't use it in the fall for my class lol

Sir Cumference

I read some Shankar too back then and it was a much better introduction

also heard good things about Griffiths QM

tbh anything other than Townsend is probably good

Dannyu NDos

As someone who had tried reading both Griffiths and Shankar, I'd say Griffiths gives more intuition, and Shankar is more mathematically rigorous.

Though, I cannot say much when they were mere tries.

Obliv

I don't really like griffiths for EM (not that I read it all the way through)

but maybe QM is better

Sir Cumference

@Obliv that's surprising, it's probably my all time favorite textbook

made every section feel intuitive

Dannyu NDos

What about CM? I don't think there is an agreement about its textbooks.

Sir Cumference

1:24 AM

@DannyuNDos as far as undergrad, I had Taylor which was mostly top notch (though its section on rotation is really not good)

Obliv

It just feels really long and drawn out lol adhd kicking in

CM I had my professors lecture slides

:D

Sir Cumference

for graduate I didn't have any book since my prof just gave out his notes instead

@Obliv same here lol

I've supposed to be studying for two tests I have this tuesday

Obliv

same lmao

Sir Cumference

but i keep getting distracted because perturbation theory is very boring

Obliv

thermo in the morning then em

Dannyu NDos

1:25 AM

I mean, I'm frustrated being taught Newtonian mechanics over and over again. Just give me Lagrangian and Hamiltonian already.

Sir Cumference

@DannyuNDos Taylor was my book for Lagrangian mechanics

though Hamiltonian mechanics is only a footnote in it, which is really stupid

Obliv

I'm still in the fun explorative part of learning physics so I can't relate as much :P

Sir Cumference

I feel like schools should mandate teaching Hamiltonian mechanics before QM

so much of the topic becomes clearer when you've seen the classical analogs

Obliv

@DannyuNDos typically from where I'm from you see it maybe once without calculus, twice with calculus and then lagrangian/hamiltonian mech lol

unless u get credit from high school for AP exam in which case u just see it once with calculus

Dannyu NDos

Yeah. And the worst thing in my institute was, they taught elementary EM without teaching multivariate calculus. Now they regret that.

Sir Cumference

1:29 AM

@DannyuNDos yeah, they did that for me too

was a nightmare

had no idea what all these crazy looking integrals and derivatives were

I basically got nothing out of my first EM class. thankfully my second one started from the beginning with Griffiths so I came out feeling much better at it

though they never went over circuitry in the second class, so my knowledge on that is empty at this point

anyways i need to get back to studying

Dannyu NDos

1:43 AM

I still haven't got used to Lagrangian and Hamiltonian mechanics. I once tried deriving the wave equation from them, and miserably failed.

In particular, I couldn't know how to interpret the continuity restriction.

naturallyInconsistent

3:22 AM

@Obliv manifestly not. Consider a solid. When T is small, U dominates, and so the system tends to lower energy, whereas when T is larger, S dominates, and the system tends to increase entropy. Two different limiting behaviours.

uhoh

5:16 AM

Only physics students will understand #physics

►

John Rennie

I prefer the right hand screw

6

nickbros123

6:30 AM

@SirCumference I read HM schey 'div grad curl and all that's before starting EM. Paid off really. Very low effort

Now thats my go to rec for pur sang physics youngsters wanting to get into em quickly

Mr. Feynman

8:12 AM

@uhoh by the way, 5 years of physics and I still can't do that

I close my eyes and imagine these vectors rotating clockwise or anti-clockwise but my hand is just not capable of such sorcery

2

user 70432

8:40 AM

I guess you wouldn't choose to teach it to students, even if it was covered in the textbook.

imbAF

9:42 AM

Can anyone help me understand how the following formula was derived:
If we are in the case of the far field resolution limit. This means that the evanescent waves are not present, as they would have damped out.
Now the condition for the propagation is : All spatial frequencies that can propagate need to be smaller than $k=\frac{2\pi}{\lambda}n$
We have a bandwidth of spatial frequencies $\DeltaK_T<\frac{2\pi}{\lambda}n$
We have a bandwidth in position space $\Delta r_T$.
From the condition $\DeltaK_T\Delta r_T>1$ one gets that:

What does it mean smallest possible localisation?

Like, that the wave is super localized ?

minimum spread?

And then we have : $NA=n sin\theta$ and from here min$\Delta r_T=\frac{\lambda}{2 \pi NA}$

How do we get the 2nd equation?

uhoh

11:28 AM

@Mr.Feynman I've always left signs as an exercise for the reader, or for someone down the hall

Sanjana

How can I show that the photon has 2 dof without going to any particular gauge?

ACuriousMind

@Sanjana All massless bosons with spin have 2 d.o.f., see this answer of mine and the respective section in Weinberg

Sanjana

Oh okay...I should have been more specific. In classical electrodynamics without going through Wigner classification stuff :)

I read that answer many times btw

ACuriousMind

then you just do proper gauge theory - "the gauge strikes twice" is a classical saying

Sanjana

I mean that's what I am after: I want to use 1. gauge transformation 2. $k^2=0$ to see that there are 2 dofs in 4 spacetime dims.

ACuriousMind

11:38 AM

if you do the constraint analysis, you have 2 independent first-class constraints in the massless case, which correspond to eliminating 2 of the 4 naive d.o.f., no going to any particular gauge necessary

Sanjana

I know how to do this in Lorenz gauge and Coulomb gauge specifically

@ACuriousMind Is there any other option? I used this up too...

ACuriousMind

what do you mean "I used this up too"?

Sanjana

I mean I know about this too

ACuriousMind

then I don't understand what more you want :P

Sanjana

In the end of this answer Qmechanic gives a short description of doing it without going to the Dirac way or the Wigner way

Neither do I know how that last two equations come, and nor do I understand what he is saying

But it seems to say that it is done without going to any particular gauge...and without using the two ways we just discussed

ACuriousMind

11:42 AM

it's more-or-less just brute-force solving the Maxwell equations without going to any gauge

the argument about the matrix shows the full solution space is n-1 dimensional, then you write down eq. (2) and observe it solves the equation and has the right amount of parameters so is the full solution, then you observe one of the parameters is pure gauge

ending up with n-2 "real" d.o.f.

Sanjana

How does he get the 2nd last equation and how does he infer that the $A_\mu^{T}$ has $n-2$ dof?

Oh you already said

ACuriousMind

(the way you "guess" that shape of the solution is of course because we know it should look like that from the other arguments you apparently don't want to use, or you can argue from the form of the equations in terms of E and B that we know we need to end up with transversal waves)

Sanjana

12:08 PM

@ACuriousMind I didn't understand how it has $n-2$ parameters yet. I got the $n-1$ part. What is the eqn $(2)$ and how does it reduce 1 parameter?

@ACuriousMind Which arguments are you talking about and can it give me the exact form of that equation?

I can get the last equation from the 2nd last one, but I want to know more about how I can guess or brute-force-solve Maxwell's equation to get that particular solution

Mah Neh

1:16 PM

Hello I wonder if someone can help me to interpret the following abstract, I'm new to this area of chemistry \ physics

arxiv.org/pdf/1601.03069

What is a "spatial grid" referred to in this context ?

imbAF

1:29 PM

Can anyone tell me what is the criterion for deciding the mode of an electromagnetci wave? Like I know TEM, which is a mode based on the fact that the k-vector is perpendicular to the electric field one. is this a standard way of determining the mode?

More Anonymous

1:48 PM

Can someone recommend me some math books?

Sanjana

@ACuriousMind I just want to clarify about this. Each first class constraint reduce two dofs. There are two first class constraints. So there are 6-4=2 dofs right?

But there are some places where they only consider the gauss law as the only constraint

Sanjana

2:30 PM

Nevermind. I found the discrepancy.

imbAF

How is it possible to have a gaussian beam, that has linear polarization?

The intensity is prop. to the electric field. Now if the electric field has i.e only the x component, because we are considering linear polarization along the x-aaxis, how is it possible to have a 2D intensity profile ?

Obliv

4:22 PM

what happens if you have a fermion and a boson in a gas? fermions obey the pauli exclusion principle but bosons dont

naturallyInconsistent

@imbAF just because an electric field only has one direction, does not mean that its field strength is only a function of that single direction.

Obliv

@imbaf physics.stackexchange.com/a/258764/73458

naturallyInconsistent

@Obliv independent variables can be considered separately

Obliv

on second thought let's not analyze Gaussian functions. They are a silly thing

Oh and it's also for same species anyway

so bosons can occupy states with bosons and fermions can't occupy states with fermions but maybe they can coexist

Mr. Feynman

5:45 PM

@uhoh "everything I say is modulo a sign"

Then there is Ultra ACM--->modulo a phase

Slereah

Modulo homotopy

Mr. Feynman

Modulo a gauge choice

Obliv

6:14 PM

what is BEC? bose-einstein C...

case?

conductor?

crystal..

nvm found it its condensate

lol

Sanjana

7:56 PM

Does anybody know a very introductory pre high-school level "Feynmanish" video/writing on Brownian motion, diffusion etc, that focuses on intuition and motivation for reading the technical subject, and describes the key points in plain English. It can be a historitcal introduction also.

More Anonymous

8:36 PM

@Sanjana Nah but if u find one lemme know as well

imbAF

10:27 PM

@naturallyInconsistent @naturallyInconsistent can you elaborate a bit more on this?

uhoh

11:01 PM

@MahNeh it's not my field, but the "basis set representation of its electronic wavefunction" means the electronic configuration is expressed as a set of coefficients, each representin how much each of the possible wavefuncions (solutions to Schrödinger equation is populated. But you can't plot that directly for visualization.

The "arbitrary spatial grid" is something you choose, and it calculates the shapes of each of the wave functions in the basis in real space on that grid of points so that you (or it) can than make a plot of it (like Figs 1, 3). I think that FIg. 4 shows an example of a grid itself.

@MahNeh Have a look around in MatterModeling Stack Exchange. There ars several chat rooms, and they are very helpful to new users and people just starting out in the field. See for example my questions How to explain to a five year old why "DFT with local exchange–correlation functionals do(es) not describe van der Waals interactions accurately"?

and Explain ab initio molecular dynamics like I'm five I noticed only two posts that mention ORBKIT explicitly but the operations it does (explained in that paper) are very common. I think you can have some success there.

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