The h Bar

2:53 AM

@Sean saw that. Wtf

Jockin john a bit too hard

despite his mad physics swag

@Sean Makes me LOL... :D

@tpg2114 WOW!! O_O

3:20 AM

I'm confused about how many basic examples I should be familiar with to "know" quantum mechanics.

What are the basic examples I should know besides particle in a box, free particle, and harmonic oscillator?

3:33 AM

@StanShunpike By knowing, if you mean you wanna get a feel about it, there's a list of systems that can be solved analytically :)

3:50 AM

@Waffle'sCrazyPeanut sweet. by knowing I mean able to derive off the top of my head.

tpg2114

@Waffle'sCrazyPeanut now there's a name I haven't seen in a really long time! How are you buddy?

4:52 AM

LOL

5

infinitesimal simplicio

Sweet :D

5:12 AM

I'm having trouble understanding Noether's theorem. Can anyone help me? For starters, I don't know what a generator is and when I clicked on the link, it took me to Lie groups. And I'm not sure how that relates. Specifically, this sentence loses me "Consider the generator of time translations Q = ∂/∂t" I have no idea what they mean by generator and ∂/∂t doesn't look like a Lie group.

5:27 AM

@DavidZ the difference between SE and other forums is that crap stays on other sites. But that was hilarious :D

5:46 AM

@JamalS I was reading this question physics.stackexchange.com/q/106605/66165 and saw your answer. Are you saying that the Dirac Lagrangian is invariant under a $U(1)$ transformation and that there is conserved current by Noether's theorem. What roles does the photon play in this?

7:13 AM

@StanShunpike You need to study some group theory before this will really make sense, but in brief, the generator of a family of transformations $U(s)$ (where $s$ is the parameter) is the operator $A$ such that any transformation $U(s)$ can be written $e^{isA}$

The generator is kind of like the normalized derivative of the transformation

So any time translation $T(\Delta t)$ can be written $e^{i\Delta t\ \partial/\partial t}$

It gets a little more complicated when you're transforming in more than one dimension (like rotations in 3D space, they have 3 parameters), but that's the gist

7:41 AM

@DavidZ Do standard mathematics books cover group theory in a way that is useful to physicists? I have two books: A Book of Abstract Algebra and Topics in Algebra. I was thinking of getting one on Lie groups, but so far the abstract algebra books haven't really helped my physics, so I want to make sure I choose a book likely to improve my physics.

Probably not, though it depends on how you define "standard"

Yeah, that hasn't been my experience.

Actually I'm told that what physicists call group theory is really "representation theory" in the mathematical terminology

There's a book on Lie groups by Howard Georgi that is pretty popular among physicists. I've read some of it, it's not bad.

I've also heard very good things about a book by Wu-Ki Tung, but I don't have personal experience with that one myself

There must be a resource-recommendation question for this ;-)

Lol should I just google resource recommendation and group theory? Yeah, representation theory isn't something I know a lot about and I definitely could use more info on.

That book list you put together was nice.

vzn pointed me to a bunch of great ones for CS. So far most book lists I have found have been through word of mouth.

Well google doesn't understand SE tags, but yeah, a search of some kind is probably not a bad idea

7:49 AM

@DavidZ That's entertaining... :)

@DavidZ btw I have increased my flagging and for the most part they have been accepted, so your recommendation to flag more often seems to have been effecfive. I didn't realize they were helpful. I was worried initially about "overloading" but that seems not to have been a problem.

@Waffle'sCrazyPeanut what kind of physics do you like?

@StanShunpike I like Astrophysics

@StanShunpike Yeah, very much not a problem here. On a large site like Stack Overflow they have more of an incentive to limit flags to the most useful ones, but here we get few enough flags that more are better

@tpg2114 Heh, apart from my academics, I'm doing great! C'mon, how did you even miss my long rant with Chris?

@Waffle'sCrazyPeanuts so are you one of those GR wizards? They use that for astro right?

7:54 AM

@StanShunpike What?!!! No, I'm not! Did you have a look at my profile? I'm just an enthusiastic amateur...

Lol I've met some pretty amazing amateurs on here :P

@Waffle'sCrazyPeanut why do you like astro?

@StanShunpike Well, I honestly dunno "why" I like astro... I've always liked stars & planets just like everyone else. That might be a reason. In fact, I have a strong belief that no one (AFAIK) dislikes astro (given its scale of interesting mysteries!)

I suppose that's true. Most of nature is interesting!

user54412

8:39 AM

@Waffle'sCrazyPeanut I think there's some truth to that. How could anyone dislike astro?

user54412

@StanShunpike Reiterating what David said:

user54412

Something useful to keep in mind: when mathematicians say "introductory group theory" they are thinking of stuff like the Sylow theorems. When physicists say "group theory" they really mean representation theory or module theory or linear algebra -- basically most of introductory abstract algebra except group theory proper. — Chris White Jan 16 at 19:21

user54412

Don't get a "group theory" math book and expect to find anything like what physicists use

user54412

of course, mathematical group theory is a great fundamental topic, and there's a reason many undergrad programs teach it first, before analysis or topology or representation theory

9:04 AM

@ChrisWhite yeah, I checked out the book David mentioned and it is a very different feel from a typical math group theory book. Much much better and more appropriate for what I am looking for. Do you have a text you like on this topic? He recommended I look around resource recommendations, which I plan on doing after I read a bit of the one he mentioned.

user54412

Alas not only can I not recommend such a book, I've never even looked at one, nor have I taken a course on this. All my physics courses skipped explaining rep theory, and my only math course on it was taught by some emeritus who went so slowly I think we defined "representation" just before the final