The h Bar

Jaime Gallego

20:00

Hello @jdbiochem

jdbiochem

:)

I have a question that's probably not suited for the Stack itself.

I'm a chemistry graduate student on a course of self-study through physics.

DanielSank

Bob Dylan The Times They Are A Changin' 1964

►

jdbiochem

My ultimate goal is J.D. Jackson's Classical Electrodynamics -- a legend among my physics grad student friends.

DanielSank

@jdbiochem Ok ask!

@jdbiochem Oh jeez. That book is awful.

jdbiochem

Awful?! Like, difficult, or actually not good?

DanielSank

20:02

I was a physics grad student as of two years ago. That book is not a "legend", it's a damned curse.

jdbiochem

Indeed.

DanielSank

It is not written in a way that helped me understand much of anything.

jdbiochem

It's the challenge! Jackson's problems are pretty amazing.

DanielSank

The problems are excellent.

(some of them)

jdbiochem

I guess we are agreed, at least somewhat.

What foundational texts / concepts might help someone approach Jackson?

I'm working through Griffith.

It seems that largely, we're talking vector calc of real fields, and PDEs in cartesian/ellipisoidal/polar/spherical/cylindrical blah blah blah

DanielSank

20:03

@jdbiochem That's a good start.

A major hurdle for E&M is crystal clear notation for all the vector calculus.

jdbiochem

PHEW

I'm glad you said it

DanielSank

I did not find that Jackson did much of a good job of that.

Griffiths at least tries.

jdbiochem

Is that why following his notation is so confusing?

DanielSank

@jdbiochem eh?

Goodness that is Dylan's best song.

You guys ever see The Watchmen movie?

jdbiochem

Yeah.

Brilliant.

DanielSank

20:06

The opening credits are amazing.

jdbiochem

The graphic novel is tops, too.

DanielSank

I was so disappointed by the rest of the movie because the credits were so good.

jdbiochem

haha

Jaime Gallego

Yes, that's where I discovered Pruitt Igoe

jdbiochem

Watchmen is maybe one of the most "literary" works in the graphic novel medium.

DanielSank

20:07

@jdbiochem I was way too young when I read it. I need to read it again now that I know some American history.

@jdbiochem Yeah, for sure.

jdbiochem

Anyway, if anybody has any favorite texts or suggestions for how to get a better grasp on approaching Jackson, hit me.

DanielSank

@jdbiochem There's a newish book... the author more or less is trying to allow us to never have to experience Jackson ever again.

It's a grad book that's sort of trying to be hard but not Jackson.

I don't recall the name/author.

jdbiochem

!!!

DanielSank

Maybe worth a look.

jdbiochem

Don't tease me.

DanielSank

20:08

Ok hang on...

I think it's this

amazon.com/Modern-Electrodynamics-Andrew-Zangwill/dp/0521896975

jdbiochem

I mean, I want Jackson for the challenge, but if there's a more modern text which doesn't rake you against the coals maybe I could get some understanding from it and take another look at Jackson.

OH!

I'm actually using Zangwill to help me understand Jackson. I'm glad you suggested it, maybe i'm on the right path.

Ch.1 in Zangwill, Mathematical Preliminaries, really helped me brush up on my multivariate vector calculus / fields

DanielSank

@jdbiochem Jackson just sucks, IMHO. The problems are good but it's really hard to learn anything useful from the exposition.

jdbiochem

Whereas Jackson just says "ok show how this vector field"

DanielSank

@jdbiochem Maybe I should buy it.

jdbiochem

I have heard that from my physics grad student friends and professors, but I have also heard that there is a great reward from pushing through it.

DanielSank

20:11

Yeah, just like there's a great reward teaching yourself to do calculus on your own. Doesn't mean you should do it that way though.

jdbiochem

It's like Goku training with a stone on his back.

DanielSank

^ That

jdbiochem

People come out the other end of the 2nd grad class on Jackson a different person.

Ben Niehoff

I think Jackson is good, but should be taken in small doses

DanielSank

@jdbiochem Yeah, depressed.

jdbiochem

20:12

hahaha

Enthused!

DanielSank

I didn't learn squat from Jackson. I mean that.

jdbiochem

Really?

Hmmm..

DanielSank

Yes.

jdbiochem

Maybe I should reconsider my priorities.

Ben Niehoff

Jackson is a mathematics book disguised as a book on electromagnetism

DanielSank

20:12

If I'd had a better teacher or something it might have been different.

@BenNiehoff But it's a crap mathematics book.

jdbiochem

@BenNiehoff, That's primarily why I'm interested in it.

DanielSank

A good math book makes you feel the math.

Ben Niehoff

the purpose of Jackson is to teach you how to figure out calculational tricks in order to complete problem sets in the time allotted :D

DanielSank

Jackson just sort of craps on your brain and then lists a bunch of hard problems.

jdbiochem

From many people, I have got the sentiment "after Jackson, my vector calc and problem solving muscles are so strong, I can crunch anything"

DanielSank

20:13

@jdbiochem Good for them! Really. I didn't get that.

jdbiochem

I'm not a physicist, but I love challenging texts.

Ben Niehoff

And by "teach", I mean "figure out on your own" :D

jdbiochem

@DanielSank Noted. Maybe I'm looking in the wrong place.

Ben Niehoff

let me tell you, I have done loads of by-hand mathematical crunching that was way harder than Jackson, but I think Jackson was valuable in preparing me for it

jdbiochem

@BenNiehoff, I am a glutton for punishment.

DanielSank

20:14

My real analysis course felt like useful mathematical weight-lifting. Jackson did not.

Ben Niehoff

do you enjoy puzzles?

Jackson is more like a book of puzzles

jdbiochem

yeah!

Yeah. I took real analysis as an elective and loved it.

While, many of the actual math majors were like "uggghh".

dmckee

@DanielSank "Close to 120 worked examples and 80 applications boxes help the reader build physical intuition and develop technical skill." I loathe texts which pull that stuff out of the narrative and make "boxes".

jdbiochem

It changed me!

DanielSank

@BenNiehoff You better believe it.

Ben Niehoff

20:15

the best problems are the ones that start "Show how to get X"

jdbiochem

Yeah!!

That's really my interest in jackson.

dmckee

Give a student with that "feature" and they'll be happy, but the won't read the book.

jdbiochem

He says "show how X" and almost nothing inbetween.

dmckee

Gah!

DanielSank

@BenNiehoff If you want proof that I like hard math problems, see my answer here.

dmckee

20:16

They need to read, and they should be given a book that encourages that, not one that discourages it.

DanielSank

@dmckee Eh?

Ben Niehoff

oh, and also things like "Sum this infinite series and get this crazy combination of sinh's and Bessel functions"

dmckee

@DanielSank Sorry. Got so worked up I forgot to include the quote I was responding to.

jdbiochem

VERY cool solution, @DanielSank.

DanielSank

@dmckee Application boxes?

jdbiochem

20:17

Random walk stochastics, sick.

dmckee

This: "Close to 120 worked examples and 80 applications boxes help the reader build physical intuition and develop technical skill."

DanielSank

@jdbiochem You read it already?

@jdbiochem Yeah, random processes is my hobby.

dmckee

In the amazon description you linked.

DanielSank

(and occasionally I need it at work)

@dmckee What's an application box?

dmckee

I imagine the book is good. It sounds like it, but those damn boxes get in the way.

jdbiochem

20:18

@DanielSank yeah. what do you like to use for modeling?

i'm a fan of R but i think there are better for stochastics, neh?

DanielSank

@jdbiochem So far I haven't needed that kind of tool. I'm a pen-and-paper type, and I use python to check my work.

jdbiochem

Nice.

dmckee

@DanielSank A "feature" of a text. A float (like a figure), but containing a mixture of text and figures itself. Usually with a colored background.

Ben Niehoff

I prefer doing things by hand for the most part, but I'm trying to learn some tools in Mathematica because some of my projects are just becoming too unwieldy

jdbiochem

Yeah, I really like the whole "as he distance to home approaches infinity" deal.

dmckee

20:20

They're used to show how the material under discussion is applied to a particular case, but they are set up as stand-alones so they break the narrative flow if you read them when you come to them.

DanielSank

@jdbiochem Here, let me show you a neat calculation I did:

5

Q: What is the connection between analog signal to noise ratio and signal to noise ratio in the IQ plane in a quadrature demodulation system?

We would like to compute the quantitative relation between analog noise near the LO frequency and the statistics of points found in the IQ plane after IQ demodulation. In order to completely understand the question we first give a detailed description of the IQ demodulation system. IQ demodulati...

@dmckee Oh yeah... those are annoying.

dmckee

If you watch a student using a book with them, you'll see that they never read the text if they think they've found the answer in a box.

And they'll apply the method in a box to problem that are nothing like the one worked in the box because they like to have a recipe resulting in all kind of abominations.

Jaime Gallego

:( This is too common in classrooms today

jdbiochem

@DanielSank WOW !

I don't really have the background to understand your answer, but the question is very interesting.

dmckee

@JaimeGallego Oh, it was common when I was in school some decades ago, too. At the lower division level, but they hadn't invaded the upper division then.

jdbiochem

20:24

@DanielSank Convolutions and kernels are something I have been trying to learn about recently for neural network applications.

dmckee

I did that "reading just the boxes" thing for a while, but I started to really learn the subject when I started reading the whole text.

Jaime Gallego

Lockhart's A Mathematician's Lament addresses this. Very good read on the situation of math education

DanielSank

@jdbiochem turns out to be reasonably simple stuff because it's linear algebra.

dmckee

@JaimeGallego A famous essay. Required reading.

jdbiochem

I really like the figure you made that shows the geometric relation between those two Gaussian point-clouds on the IQ plane

makes it very clear

DanielSank

20:28

@jdbiochem thanks. Diagrams are darn helpful things.

0celo7

20:41

@JaimeGallego never heard of it, what's it about?

Jaime Gallego

@0celo7 An analysis of K-12 math and how it's depriving students of real mathematics

Quite insightful

Emilio Pisanty

@DanielSank what the hell is an "IQ demodulation"?

actually, no, I'm not really asking

but I do want to express wonder at a world that gives birth to such abominations =P

0celo7

@dmckee This is sadly true.

DanielSank

21:22

@EmilioPisanty It's just a way to get the amplitude and phase of a signal.

@heather!

@dmckee I usually skipped the boxes entirely.

heather

@DanielSank hello

@dmckee ugh, i hate out of narrative in text boxes, but for a very OCD reason

dmckee

The strange thing is that I know few physics professors who like them, but the textbook people advertise them as a feature. What gives?

heather

i have to read all the text on one page before going to the next page, and so i've got to read the boxes. but if the last sentence goes onto the next page, you have to stop one sentence before, read everything else, and then read what's next. Or you can start with the boxes, but generally you have to know what's going in the main text to read the boxes ::shivers::

@dmckee it sounds like a feature to the administrators who have to pay for them?

dmckee

@heather Ooph. I'm sorry to hear that.

It is tough going to change a habit of mind like that.

heather

21:42

yeah, hopefully as I read more textbooks I can break that habit

but I always prefer a book with a simple page layout.

loltospoon

Hello again

So I think I've finished writing that program

that approximates energies

for the infinite square well

now I'm wondering: what would the boundary conditions be for a potential $V(x) = V_0$ for $x \in [a/2,a]$?

where the length of the well is $[0,a]$

ACuriousMind

....why is your well located at $[0,a]$ and the potential at $[a/2,a]$?

Also, since it's an infinite well, what do you think the boundary conditions should be?

loltospoon

@ACuriousMind wait yea, I just realized that. I meant a situation without $V=\infty$. So imagine a free particle that reaches a step potential. Let's say the step potential continues past $x=a$. What, then, is the boundary condition on the right?

Jaime Gallego

I am the very model of a singularitarian

►

loltospoon

With the infinite square well it was easy: the wavefunction must be zero on the right because the potential is too high. But then what boundary condition occurs for a step potential?

ACuriousMind

21:52

@loltospoon Okay, for a step potential, you chop up the problem into three areas (pre-step, step, post-step) and then impose that the wavefunction itself and the first derivative match at the boundaries of those areas.

loltospoon

@ACuriousMind Ohhh ok

so nothing special occurs post-step

The interesting stuff, i.e. the stuff we make into boundary conditions occurs whenever the potential changes

Emilio Pisanty

@ACuriousMind One minute twenty seconds

you're slipping

0

Q: Electron ,Electromagnetism & Quantum mechanics

what makes electron not losing its energy, as by electromagnetism it should radiate, & not falling down to the nucleus,even down from the Bohr's atomic radius? or is it possible to change the physical definition of electric charge to make the Borh's assumption valid under Electromagnetism? i know...

quantum-mechanics electromagnetism electrons atomic-physics orbitals

ACuriousMind

@EmilioPisanty That was in January. Maybe I'm improving ;)

Emilio Pisanty

@ACuriousMind ah, right you are

then yes

Anyone recall a recent question about whether the projectors of commuting observables commuted?

ACuriousMind

22:11

@EmilioPisanty physics.stackexchange.com/q/315564/50583 ?

0celo7

@ACuriousMind What does it mean to take a Laurent series "at infinity?"

Specifically, of $$\zeta\mapsto \frac{1}{\zeta-t},$$where $t\in\Bbb R$ is fixed, $\zeta\in\Bbb C$.

ACuriousMind

@0celo7 Probably to consider the function as a function on the Riemann sphere, then expand around the pole of the sphere corresponding to infinity.

0celo7

@ACuriousMind I haven't proved that my function is continuous on the Riemann sphere...

it is a Laurent series in $\zeta^{-1}$?

ACuriousMind

@0celo7 Well, then either claim it's obvious or prove it :P

0celo7

actually I want $(t-\zeta)^{-1}$ above but whatever

@ACuriousMind It's actually an operator valued function, and none of this is obvious :P

I'm trying to do it more simply first

ACuriousMind

22:17

@0celo7 If your $\zeta$ is the "standard" coordinate on the complex plane, then yes.

0celo7

@ACuriousMind so if I write $f(\zeta)=(t-\zeta)^{-1}$...what would it be?

A smart man told me it's $$-\sum_{n\ge 0}\zeta^{-n-1}t^n$$

and that holds for $|\zeta|>|t|$

unfortunately I am merely a poor farmer and don't understand this

ACuriousMind

@0celo7 Well, write it as $f(z) = (t - z^{-1})^{-1}$ and compute the Laurent series of that around $z=0$.

Then replace $z = \zeta^{-1}$ in the end.

0celo7

Clearly.

So I need to do all of the integrals?

Or is there some trick?

$$f(z)=\frac{z}{tz-1}$$

ACuriousMind

I was just about to tell you to write it like that!

0celo7

Probably best to scale $z$

@ACuriousMind I hate complex analysis.

ACuriousMind

22:24

Now you just need to know the standard series for $1/(z-1)$ and you're done.

0celo7

Ahhhh

Because I'm expanding around $z=0$

So that's just the Neumann series

@ACuriousMind That gives the correct answer.

AccidentalFourierTransform

@loltospoon sup

0celo7

@ACuriousMind I think I read this somewhere but I can't find it again: the spectral radius is $\le$ the operator norm regardless of the norm?

That seems very wrong

@ACuriousMind Finite dimensional spaces

ACuriousMind

@0celo7 Why does it seem wrong?

0celo7

@ACuriousMind It doesn't. The operator norm is very powerful.

There's a lower bound provided by the largest eigenvalue.

(which might be zero but hey)

@ACuriousMind how do I draw a zeta? Mine end up like less crazy xis.

ACuriousMind

22:35

@0celo7 Also, the (finite-dimensional) proof of that is right on the Wiki page of the spectral radius :P

loltospoon

@AccidentalFourierTransform hello!!

I was going to ask you something

0celo7

@ACuriousMind My definition of the spectral radius is more complicated, I think it's supposed to help when we do $\infty$-dimensional perturbation theory.

ACuriousMind

@0celo7 "Like a little ballon"

loltospoon

oh! so it turns out that I didn't need matrices/diagonalization

ACuriousMind

That's what I was taught

0celo7

22:36

But I do know that it's equal to the largest eigenvalue, and the operator norm is always larger than all of the eigenvalues.

It follows that $\mathrm{spr}\, T\le ||T||$.

But I'm just checking.

loltospoon

@AccidentalFourierTransform apparently, once we generate the wavefunction we essentially already "know" the allowed energies. We were guessing an initial energy to solve the differential equations, so once our generated wavefunction met the boundary condition on the right side, we say that the initial energy guess must be an allowed energy.

0celo7

@ACuriousMind I'm retarded. I have $\mathrm{spr}\, T=\inf\{||T^n||^{1/n}:n\in\Bbb N\}$.

@ACuriousMind what?

@ACuriousMind who taught you that??

AccidentalFourierTransform

@loltospoon well, that definitely doesnt sound right, but if that is what your professor expected, so be it

ACuriousMind

@0celo7 My Ancient Greek teacher :P

AccidentalFourierTransform

Shooting method

In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to the solution of an initial value problem. Roughly speaking, we 'shoot' out trajectories in different directions until we find a trajectory that has the desired boundary value. The following exposition may be clarified by this illustration of the shooting method. For a boundary value problem of a second-order ordinary differential equation, the method is stated as follows. Let y ″ ( t ) = f ...

ACuriousMind

22:39

I'd show you but I'd have to get my tablet and it's across the room :P

AccidentalFourierTransform

@loltospoon what you did is similar to ^

0celo7

@ACuriousMind :( ok

ACuriousMind

Maybe I can find one somewhere in what I have already written

0celo7

@ACuriousMind look at this horror

AccidentalFourierTransform

thats not a zeta, thats a xi

0celo7

22:42

I know!

I need help!

AccidentalFourierTransform

or use a $z$ for complex variables, like everybody else

0celo7

nope

screwthat

ACuriousMind

AccidentalFourierTransform

not bad

0celo7

@ACuriousMind from string theory I bet

Casimir?

ACuriousMind

22:43

@0celo7 Statistical Physics, actually

0celo7

When did you take a stat mech class??

ACuriousMind

That was...damn...three years ago

AccidentalFourierTransform

once upon a time

ACuriousMind

I didn't learn much except computing random integrals, the class was horrible

0celo7

@ACuriousMind We met two years ago!!!

It's been a long time

@ACuriousMind how tf is that a ballon, anyway

ACuriousMind

22:46

I did remember that one of the assignments contained $\zeta$-functions, so I guess it was good for something :P

@0celo7 The loop at the top is the ballon itself, the rest the string by which the child that lost it held it.

0celo7

I don't think the simile works in English.

ACuriousMind

Not sure it works in German, either :P

0celo7

how is the loop at the top a ballon?

ok in the second line from the bottom I think I have a really good one

AccidentalFourierTransform

you have three good ones

ACuriousMind

^I concur

lol, I put "Nope." as the answer to several questions of the form "Compute X" on these assignments.

No idea how I passed that class with a good grade :P

0celo7

22:53

Seriously?

Pic?

@ACuriousMind I wanted to do that on my QM midterm yesterday. Eight-fold degenerate perturbation theory with two perturbation terms. Ugh.

I'm pretty sure everything I did was wrong.

ACuriousMind

Well, we only need to get 50% of the points on the assignments to get admitted to the exam, it doesn't actually pay off to get them all right

Except for bragging rights :P

0celo7

Admitted to the exam?

ACuriousMind

@0celo7 If you haven't gotten 50% on the assignments, you're not allowed to take the exam in many of the courses.

0celo7

@ACuriousMind How much is the homework worth for the final grade?

ACuriousMind

Also, the exam is usually the entirety of your grade, doesn't matter how good you were on the assignments

0celo7

22:56

Oh, very different system.

In my classes the homework is ~30% of the grade.

I think in my analysis class it's 60%.

ACuriousMind

Sometimes there's a tiny bonus for being good at the assignments, but usually not

Many of the more advanced classes don't have mandatory assignments at all

0celo7

@ACuriousMind Yeah, that's the way my algebraic topology class is right now

ACuriousMind

That is, there are exercises, but they aren't graded at all, just discussed in a class.

0celo7

The elven lord is just preaching about knots right now, not sure what homework we could even have

ACuriousMind

"Tie your shoes" :P

0celo7

22:58

@ACuriousMind Tie one with a right-handed trefoil and the other with a left-handed

@ACuriousMind terms $\sim z^{-2}$ don't show up in the residue theorem, right?

ACuriousMind

@0celo7 right

@0celo7 He could always make you tie his eponymous unknot

0celo7

@ACuriousMind Did I tell you I met his son?

ACuriousMind

Oct 12 '16 at 18:30, by 0celo7

@ACuriousMind So I met the Elven Lord's son

Yes :)

0celo7

@ACuriousMind Hmm.

I'm not so sure that's actually his son :P

The dates don't make sense at all.

They're only 5 years apart in age :P

I'm 99% sure he said he was his son lol

@ACuriousMind how awkward would it be if I asked?

ACuriousMind

If they are only 5 years apart it would appear very awkward, I think

0celo7

23:09

I'm confused.

Forget anything about his son then

topic change

dmckee

Is there a polite way to say, "Now, look, you. You clearly don't have the first clue about the problem domain you're trying to lecture me on and have to go back to square one and start with the ABCs."?

Just an idle thought.

Jaime Gallego

@ACuriousMind Well see, Einstein at age five...

:D

ACuriousMind

@JaimeGallego not that again :D

@dmckee Nah, the whole good feeling that sentence gives you is because it is not polite ;)

0celo7

@ACuriousMind well maybe he had a kid and had to take off from school

And only got around to getting his PhD after his son went to college

He did speak about teaching algebra at the London Printers Association once

ACuriousMind

@0celo7 You know, it's not actually hard to find a picture of the son to check whether that was who you saw. Train your google fu!

Slereah

23:31

Help

I am ill once more

loltospoon

@AccidentalFourierTransform wow that sounds exactly like what my professor described lol

0celo7

@ACuriousMind the guy I think is his son has a different name

He's been married at least twice

I do have Google fu, master

@Slereah wtf? What happened

Slereah

23:52

Germs and microbes invaded my body and now I am ill

Yassin Rany

hey guys

someone here:

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