The h Bar

Silly Goose

18:00

@TobiasFünke thanks, cya around

@naturallyInconsistent i think yes. Is the extended zone scheme just plotting the dispersion $E(\vec{k})$ as a function of arbitrary wave vector?

naturallyInconsistent

@SillyGoose for now, you can think of it that way

Silly Goose

is there not a CMT book that just lays out everything precisely :P I do not care if it is not pleasant to read

while reading both A&M and G&Y, I get the feeling that I am fed little bits at a time...

naturallyInconsistent

Now, in the periodic empty lattice that you are considering using extended zone scheme, it is fact that, because of the periodicity, anything outside of 1BZ is pretty much fiction. They can all be mapped to 1BZ, but the cost of this mapping is the introduction of the band index

Silly Goose

also A&M seems to quickly brush over (in general) introducing concepts. like only a few pages are spent introducing energy bands in chapter 8.

naturallyInconsistent

@SillyGoose The problem lies on your end. A&M is clear on this, Kittel is clear on this, and for what I saw of your G&Y snippets, it is even better.

Silly Goose

18:04

It is extremely unclear to me :P

naturallyInconsistent

Now, let's get back to myow exposition

@naturallyInconsistent @SillyGoose do you agree with this and understand this?

give meow a moment, gonna get the laundry

Silly Goose

@naturallyInconsistent I don't think I necessarily agree that the band index solely comes from mapping back into the 1BZ. I thought that the band index is argued to appear before any discussion of mapping $\vec{k}$ into the 1BZ. I agree that you can always map $\vec{k}$ into the 1BZ.

naturallyInconsistent

@SillyGoose Well, yes, in Bloch's theorem, you need the band index, but that is because the $\vec k$ in Bloch's theorem is itself restricted to 1BZ, amongst other things. Once you have that restriction, you must have band index, just to get back the correct number of degrees of freedom. Like, you started with 3N total non-interacting electrons, you must be able to get all of them, and no more.

Silly Goose

@naturallyInconsistent I would then agree that mapping back into the 1BZ utilizes the band index (but does not solely contribute to it).

@naturallyInconsistent hm well the statement of Bloch's theorem I use does not restrict $\vec{k} \in \text{1BZ}$

Or, okay well I guess maybe A&M uses that statement of Bloch's theorem.

naturallyInconsistent

Good. At least we are progressing. The mapping from extended zone scheme to reduced zone scheme is the thing that we are doing by this mental exercise right now. Note that there is a subtlety involved: we call it folding, but there is absolutely no folding operation at work. Folding a paper in two includes mirror reflection of a part. There is no bit of that. Instead, it is strictly cutting, and rigid translation.

@SillyGoose We will come to that. You must let meow finish the dayum introduction, FFS

Do you at least agree that, by the procedure above, we at least arrive at the reduced zone scheme with band index, that it is sensible and aint just baloney?

Silly Goose

18:15

Yes I have no problem with the reduced zone scheme as you describe and as is written quantitatively by G&Y in an above screenshot.

Well no problem understanding its construction. I am yet to find out its usefulness.

naturallyInconsistent

Good. In a real crystal, the original electrons (but still non-interacting), even in the extended zone scheme, do not just make up the single mass shell. There are many bands even in the extended zone scheme, necessitating the band index even in the extended zone scheme.

Can you see why it is useful, now, to just give up and be happy with having a band index?

Silly Goose

That I have no problem with.

I do not have a problem with what i will call real energy bands coming from band indices that appear in the extended zone scheme

naturallyInconsistent

Then, why are you asking that original question in the first place?

or do you only understand it now?

Silly Goose

I have since the beginning only had a problem with what I will call artificial energy bands appearing due to using the reduced zone scheme

Which is why I use the free particle example. In the extended zone scheme, there is a single energy band.

naturallyInconsistent

Well, there are MANY reasons.

Silly Goose

18:24

In the reduced zone scheme, there are an infinitude.

naturallyInconsistent

All of which are just about you not soldiering on to read the next chapter

Silly Goose

I mean I am trying to make sure I understand the basic concept before moving on

To me that is an insufficient definition being provided of the basic concept. An example should clarify, not add additional information to the definition itself.

naturallyInconsistent

Well, again, you cannot yet see the utility because the extremely obvious utility is in the next chapter

Silly Goose

Also I did do this move on and see method while sitting on the lectures this (just ended semester), to no avail.

naturallyInconsistent

this whole exercise could have been omitted if you would just read on...

Silly Goose

18:27

Separately, is the Fermi energy and Fermi surface (according to Ashcroft & Mermin) only defined at $T = 0$?

They talk about "ground state" but I don't know if that's supposed to implicitly mean at $T = 0$

naturallyInconsistent

If you focused solely upon the extended zone scheme with just one single band, then the next chapter will present itself as incredibly mysterious. However, with either the reduced zone scheme or periodic zone scheme, the behaviour is strikingly obvious. That's the point of their introduction.

Silly Goose

@naturallyInconsistent Okay well I will move on for now

naturallyInconsistent

@SillyGoose Fermi energy $E_F$ is defined as $\lim_{T\to0}\mu$ (electro-)chemical potential and the Fermi surface only exists in normal metals, the existence of which then defines that the material is a metal.

Silly Goose

why do A&M not define it that way ;_;

naturallyInconsistent

@SillyGoose ??? By your wording, it seems like you had already reached the use, yet you said that the semester just ended, and so actually you havent yet seen its use?

@SillyGoose I think it does, just a bit later.

Silly Goose

18:31

@naturallyInconsistent well we didn't really look at many band structures and what not. (i was just sitting in on the lectures also, didn't take exams or do the hws)

naturallyInconsistent

A&M is a really wonderful book to read...

Silly Goose

we did a graphene tight-binding computation and even then i didn't really see what use there was of restricting k to 1BZ (or notice if we even did)

but i think this course followed A&M pretty closely, so i probably just missed it

the latter half of the semester was on semi-classical stuff where we kind of left the bravais lattice machinery behind

but again i could just be missing it all

@naturallyInconsistent sad why not just introduce it properly in the first place. this is my problem with this book and G&Y

naturallyInconsistent

@SillyGoose Ok, I'll give you the reason up-front. We really don't care about the empty lattice. But when you introduce a tiny interaction, the extended zone scheme paraboloid sheet develops breaks into many disconnected bands at many places, and that is entirely mysterious until you realise that in the reduced zone scheme, they are precisely those areas where the $\vec k$ point in the 1BZ is the same and the energies are the same, then there is a repulsion between energy bands opening up a gap.

Silly Goose

@naturallyInconsistent Okay I can buy into this. I do recall this being stated in lecture but I don't think I followed the arguments leading to the claim. So I will (hopefully) find an explanation of this in A&M.

naturallyInconsistent

@SillyGoose That's not how education works. Do you expect your age 10 school teacher to start with set theory and directly construct non-negative integers, taking 400 pages to finally prove that 1+1=2 and nothing other than 2?

Silly Goose

18:36

@naturallyInconsistent i mean this is a graduate solid state class. assuming undergrad stat mech is fine, i would think.

naturallyInconsistent

@SillyGoose grrrr!!! If you have already heard this, then you already had more than enough material to piece together the answer yourself!

Silly Goose

@naturallyInconsistent well i don't understand the fact, nor till you said it here recalled that it had to do with workign in the reduced zone scheme

naturallyInconsistent

@SillyGoose On the contrary. A lot of graduates come back to university after a stint in industry, and so they cannot remember the depths. i.e. in a uni with 4 year BSc, 4xxx mods tend to be more intense than 5xxx mods.

@SillyGoose Look, this is also why textbooks and educators who actually know how it is to teach, do not just state the final definitions right at the start. People who do that get lynched, and they deserve the mob.

Silly Goose

That is true, but at this institution this solid state course is generally filled with 2nd and 3rd year graduate students (who were required to take graduate stat mech first year). I think this year there were an unusual number of first years, perhaps owing to the fact that the first year cohort is quite large.

naturallyInconsistent

Students deserve the understandable storyline

Silly Goose

18:41

But that is just not how I learn :P

naturallyInconsistent

manifestly not, since you just told meow that the lecturer mentioned the reason to you, and you didnt understand it and thus could not recall it.

Silly Goose

Separately, to have two or more partially filled bands at $T=0$, do you need energy bands to intersect?

think_meaning_buildß

@naturallyInconsistent 365 pages, actually :P

Silly Goose

I am not claiming against an understandable storyline

naturallyInconsistent

Well, what is the precise definition of "intersect" being used here? The original non-interacting electron bands? Or the definition where bands are strictly counted upwards from lowest and thus rarely intersect? Or you collapse the bandstructure into smeared out bands and thus any energy overlap is an intersection?

Silly Goose

18:45

I am claiming that what is understandable is quite different for different people

naturallyInconsistent

@think_meaning_buildß surely not such a nice number?

Silly Goose

I am trying to think of a heuristic example of what leads to this situatio

naturallyInconsistent

@think_meaning_buildß suspicion vindicated: ✱54.43: "From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2." – Volume I, 1st edition, p. 379 (p. 362 in 2nd edition; p. 360 in abridged version). (The proof is actually completed in Volume II, 1st edition, page 86, accompanied by the comment, "The above proposition is occasionally useful." They go on to say "It is used at least three times, in ✱113.66 and ✱120.123.472.")

think_meaning_buildß

ok 360ish

naturallyInconsistent

@think_meaning_buildß look, a brit!

@SillyGoose where is this from?

Silly Goose

18:48

@naturallyInconsistent A&M section 8.7

think_meaning_buildß

Whitehead had some memory heavy ideas about how maths should be taught

naturallyInconsistent

@SillyGoose you don't have to think, you know? I think somewhere they would have Aluminium as an example of a nearly-free-electron (NFE) with a Fermi surface that has both 3rd and 2nd bands bits

@SillyGoose The snippet literally said that in Chapter 12 it will be seen that Fermi surface existing -> metallic properties.

Silly Goose

i am not sure what you mean

naturallyInconsistent

@think_meaning_buildß that's why the head turned white. Do not follow.

@SillyGoose which is this referring to?

Silly Goose

i am trying to think of what the band structure looks like to allow at T = 0 for multiple bands to be partially filled via filling up bands electron by electron from lowest to highest energy.

I concluded that to have two or more partially filled bands, bands would need to intersect. That is what I am wondering if true or not

this is a sketch of what I mean. two bands $m$ and $n$ intersect such that the fermi energy lies above both such that both are partially filled

think_meaning_buildß

18:52

@naturallyInconsistent He wrote an intro to algebra textbook that never caught on.

inspired by the Bourbaki, I believe.

naturallyInconsistent

@SillyGoose In your example, what will end up happening is that the whole pink bits become the lower band, and the white bits are the top band, and then the part where they cross, if not protected by symmetry, would form a repulsion, and then there is no overlap.

Have you done the simple example of the empty lattice, where you draw circles on a square grid, and then do the BZ-folding and see for yourself that there will be parts of the Fermi sphere that is in 2nd band and part in 3rd band?

Relativisticcucumber

@TobiasFünke i tried to answer the q based on your comment. is this what you meant? physics.stackexchange.com/a/837970/337317

/ did i get it right xD

also @naturallyInconsistent you had thoughts on this as well. i just wanna make sure im correct xD

naturallyInconsistent

@Relativisticcucumber you are correct. But you missed the huge discussion we just had on the topic here, and it turns out the wacky fowl is outright being silly and forgetting that he heard the answer from the lecturer. His actual question is thus totally different from what is stated anywhere in his post.

Silly Goose

my post states my original question

Relativisticcucumber

@naturallyInconsistent well maybe it can help another lost soul lol

@naturallyInconsistent on par with the bingo meme

naturallyInconsistent

19:06

@Relativisticcucumber well, I literally never managed to get to the important point: why there would be more than one band even in the extended zone scheme. This sucks so much.

Relativisticcucumber

:o

naturallyInconsistent

@Relativisticcucumber oh, miao miao just learnt that "goose" implies female. Guess why miao miao just learnt this.

Relativisticcucumber

:O i just learned that as well wow

@naturallyInconsistent i have no hypothesis xD

pls no sexy time w geese 0.o

naturallyInconsistent

@Relativisticcucumber because the wacky fowl's question today really ought to be cause for some slight licking by flames. But miao miao forgot the phrase, and instead searched for the one that mentioned gander, and thus learnt that gander is male goose.

so yeah, the next time ya meet, throttle the wacky fowl for meow

just a bit

Herr Feinmann

@TobiasFünke not quite. My mind is still grinding

Relativisticcucumber

19:13

@naturallyInconsistent lol

naturallyInconsistent

@HerrFeinmann still better than

Cymbal Monkey Homer Simpson

►

Herr Feinmann

@naturallyInconsistent I'm slowly coming to terms with the idea of inconsistent definitions over literature and the matter still being discussed as of today. Then I want to ask you, how I am supposed to read papers and compare result if I don't understand the conventions in the first place? D:

naturallyInconsistent

Don't read those papers. You'll thank meow for the decades of extra stress-free life

ACuriousMind

@HerrFeinmann very carefully ;)

naturallyInconsistent

Another way out is to always ignore other people's conventions and so reproduce important results yourself in your own convention.

Herr Feinmann

19:17

Please tell me that these conventions do not alter the results D:

naturallyInconsistent

crickets chirping

(because unlike a certain suspended individual, miao miao is not in the business of confidently stating something that miao miao is unsure about)

Herr Feinmann

This is the day in which I learn that some branches of physics are not unlike astrology

2

naturallyInconsistent

lol

let's get that starred

Herr Feinmann

Wait, has RR been suspended again?

And how did I guess who? :P

naturallyInconsistent

@HerrFeinmann wipes musket

Herr Feinmann

19:19

Bloody ACMary

3

Silly Goose

i hope to find some method in this madness of CMT...

Herr Feinmann

Give up and start guessing things using the positions of the stars

naturallyInconsistent

@SillyGoose look, the thing you are having a headache now on, is a beautiful and fully understandable complete theory that can always be made exactly rigorous to any mathematical standard you like it to be. Herr Feinmann's (and yes, miao miao will annoy him with that spelling until he changes it to something nicer) current headache is an unsolved physics convention fistfight that had endured for half a century or more.

think_meaning_buildß

BKFC

Relativisticcucumber

ACuriousMind

19:25

@SillyGoose if it's any consolation to you I find the whole language of condensed matter also rather confusing :P

Relativisticcucumber

i am trying to parse through what this highlighted section is saying -- why can a singlet lower its energy by tunneling but a triplet state does not allow this?

@ACuriousMind theres a commonality btwn u guys

a lack of worship of experiments

Herr Feinmann

@naturallyInconsistent ファインマンさん could be problematic

By the way, nI, this is a recurring issue in my life.

Relativisticcucumber

@HerrFeinmann recently i was berated for saying that astro(nomy) was easier than some other fields of physics -- my colleagues claim that no field of physics is easier than another. i think they are delusional but ill never speak my thoughts there again :P

naturallyInconsistent

@HerrFeinmann what part of nicer do you not understand?

Herr Feinmann

[physics.stackexchange.com/questions/716754/… younger me)

@Relativisticcucumber hey, I said astrology!!!! :P

naturallyInconsistent

19:30

@Relativisticcucumber oh lol, you, you have definitely never attempted something horrifying in astronomy. There are sooooo manyyyyy

Herr Feinmann

@naturallyInconsistent 费曼先生

Relativisticcucumber

@HerrFeinmann yes but it gave me flashbacks

Silly Goose

@ACuriousMind i am having an impulse to look to a QFT book to learn CMT from...

Relativisticcucumber

@naturallyInconsistent i mean surely every field has smth atrocious

naturallyInconsistent

@HerrFeinmann that is nice for meow meow but surely it aint nice for most others here

Relativisticcucumber

19:32

i just dont buy into this idea that no field is harder than another

Silly Goose

i think you should define "harder" @Relativisticcucumber

Herr Feinmann

Oh, so in Chinese 先生 is "Mr."

naturallyInconsistent

@Relativisticcucumber well, have you tried solving Kepler's impossible equation?

Relativisticcucumber

@HerrFeinmann it's sir, no?

Herr Feinmann

In Japanese it's something else

It usually means teacher

Relativisticcucumber

19:33

laoshi is teacher in chinese

Herr Feinmann

Although the etymology is the same as the Chinese one of course: "who lived before"

Relativisticcucumber

老师

Herr Feinmann

(I guess)

I can't write these hanzi :(

ACuriousMind

@Relativisticcucumber Some things are easier for some people than others; I would be careful to claim that there is such a thing as universal difficulty of a subject

naturallyInconsistent

生 here means birth, 先 means earlier, i.e. this guy is born earlier. Makes for a good reason why they are the teacher, sensei. The earlier is also why you have sempai for senior, even if it is just the mildest of seniority

Herr Feinmann

19:35

Yes, that's what I was talking about above. I was astonished when I realized that

Even kanji combinations are more logical than magnetic works :P

Relativisticcucumber

@ACuriousMind i just think this is kind of absurd tho. so since i have 5 years exp in neuroscience research i made the claim that neuro research is much easier than physics and even the physicists wouldnt agree w this. i mean if i can do the research as a 16 year old it's just obviously easier (on average). of course things are relative but that doesn't preclude making assumptions about average behavior

ACuriousMind

@SillyGoose that will probably also not do what you think it will do - the best possible outcome is that you stick with hep-th QFT instead :P

naturallyInconsistent

@Relativisticcucumber old leader, which makes sense to be teacher

@HerrFeinmann kanji took millennia to form. Obviously some sanity was imbued in parts.

Relativisticcucumber

@naturallyInconsistent yeah i feel like the chinese language really reflects cultural ideas of the society which is interesting

naturallyInconsistent

@SillyGoose it will just compound your problem. Just as ACM said

@Relativisticcucumber have you considered a different viewpoint: that the specific research that you were doing, was simply easier to do than is representative of the field as a whole?

ACuriousMind

19:38

@Relativisticcucumber all languages reflect cultural ideas, you just usually don't think about the ones in your native language :P

naturallyInconsistent

Like, successive generations of CMT people are trained to start with defects in solids, as a simple thing to play with, before going on to something more difficult.

Relativisticcucumber

@naturallyInconsistent yes. but i still think the statement "cellular neuroscience research is on average easier than experimental condensed matter research on average" is true.

@ACuriousMind bah i do wish i could experience things about my culture from an outside perspective. sadly it seems difficult

naturallyInconsistent

@Relativisticcucumber at some point it would run into what ACM is trying to tell you: do you even have a metric with which to measure, even extremely vaguely, which way is which on this matter? What does your statement even mean?

Relativisticcucumber

i mean if nothing else, i can define a notion of "average difficulty" and invoke the idea that there's no way everything measures equally on any given scale, so therefore something must be "on average easier" than another thing.

ACuriousMind

@Relativisticcucumber Okay, so there's already 2 subtleties here: 1. You're kind-of equating difficulty with how much you'd have to learn beforehand to do something and 2. obviously one only lets a 16-year old do research suitable for that 16-year old (if one is responsible). I would agree there's probably more help that a 16-year old can provide in the average neuroscience lab than in the condensed matter lab. I'm not sure what exactly that tells us.

Relativisticcucumber

19:42

@naturallyInconsistent true lemme provide the context

think_meaning_buildß

@HerrFeinmann taking quality control to a whole new level :P

Relativisticcucumber

lemme explain. so there's a person at my uni who is extremely condescending to others. one of my friends said, 'its ok if shes condescending bc shes really smart" then i replied "what data makes you say that" (bc i dont know the person well) then my friend replied "shes a year ahead in her research program" then i said "well it's easier for her to be a year ahead bc she is doing astro" then i defined easier to mean "A is easier than B if A has less prerequisites to [...]

[...] get to a point where one can do practical research in a field than B". namely i was trying to point out that saying someone is smarter because they are "more ahead in research" doesn't make sense when a second year student being "ahead" likely means they had many less prerequisites to meet.

ACuriousMind

I'm not sure I even understand what being "a year ahead" in a research program means :P

but I think the idea you should be attacking here is not that the condescending person is smart, but that it's okay to be condescending just because one is smart...

Silly Goose

there are indeed many things wrong with the situation he

naturallyInconsistent

@think_meaning_buildß do you know what you order at the bar if you can't have any alcohol?

think_meaning_buildß

19:50

water?

Relativisticcucumber

@ACuriousMind well yes but im more appalled by the general reluctance of people to consider the possibility that some things are harder than others

naturallyInconsistent

lol no, if you're already at a cocktail bar and it is all high class, you can't be ordering something like water or juice

think_meaning_buildß

a virgin ~~bloody~~ mary?

naturallyInconsistent

@think_meaning_buildß why would the virgin be bloody? just virgin mary would do

Relativisticcucumber

@naturallyInconsistent is this a joke

naturallyInconsistent

19:53

@Relativisticcucumber yeppuu~

but it's a useful trick to learn, when in a social situation where you want to do some pretending

ACuriousMind

@Relativisticcucumber Well, see, my personal reluctance is exactly because essentially the only reason this is ever relevant is because someone wants to say "A is harder than B, and I can do A, so I'm better than you" (as in your case!)

think_meaning_buildß

@naturallyInconsistent the tomato juice makes it look bloody, no?

ACuriousMind

I don't see why this notion would ever come up except in useless status battles

naturallyInconsistent

@think_meaning_buildß yeppuuu, and I think there is some catholicism reference to have called it that, miehehehe

ACuriousMind

We can talk about what you need more or less prerequisites for to work usefully in, of course, but to brand this in terms of "easier" and "harder" is exactly one of those culturally loaded distinctions I'd prefer to avoid

naturallyInconsistent

19:59

@Relativisticcucumber It is just not the case. The standard go-to stereotype that plebs think of geniuses, are neurosurgeon, rocket scientist and nuclear scientist. That means that even in the public consciousness, there are fields of study that are renown for difficulty. What people are pushing back against isnt the notion that there can be differences in difficulty, but rather what ACM is picking out.

Relativisticcucumber

@ACuriousMind ermmmm. i dont think id think "im better than you", but there are many times in my life where i set out to do smth hard, and i do it, and i am proud in the end that i can do that. i dont see what's wrong w that.

ACuriousMind

@Relativisticcucumber I don't think there's anything wrong with that, but why is your pride contingent on the thing being objectively "hard"? Can't it just be "I worked hard for that" instead of "this thing is objectively hard"?

Relativisticcucumber

@ACuriousMind because if i work hard to do smth not hard then i feel pathetic xD

ACuriousMind

yeah, that's what believing in objective difficulty will do to you :P

Relativisticcucumber

i think most people feel some type of internal validation along these lines, no?

think_meaning_buildß

20:06

yes

Herr Feinmann

I prefer to think that everything I manage to do is actually easy precisely because I did it :P

Relativisticcucumber

LOL thats even sadder

ACuriousMind

@Relativisticcucumber yes, but I do believe very strongly the validation comes from your own feeling of having worked hard, not from the thing being intrinsically hard

think_meaning_buildß

I did it my way!

Herr Feinmann

@Relativisticcucumber yeah, I fuel myself with self-deprecation

Silly Goose

20:08

@think_meaning_buildß and now the end is near~

Herr Feinmann

My goal is to reach an "acceptable" level :P

Where "acceptable" is defined as my current level+1

naturallyInconsistent

@think_meaning_buildß over the years, that song really really attracted the worst kinds of people, so much so that the daughter of the singer had to remind them what the first line of the lyrics was.

think_meaning_buildß

but the repetition of "I did it my way!" is what sticks

Relativisticcucumber

@ACuriousMind hmmmm

naturallyInconsistent

well, that is the time to remind oneself that there are plenty of historical examples of people spending 20+ years slogging away at a problem and arriving at a good result, but that the result is eventually replaced by a better scheme that achieves better results in shorter time. Of course, the invention of modern computers made for a LOT of these stories.

Relativisticcucumber

20:14

i mean sure, to some degree. i think if i woke up and could just magically solve all of the worlds hardest problems it wouldnt have the same degree of satisfaction as if i worked a lifetime for that. but it certainly wouldnt give me no satisfaction

think_meaning_buildß

lest we forget the old saying, "possession is 9 tenths the law" and "my way" belongs only to me

ACuriousMind

@Relativisticcucumber This will come off as bragging but it will perhaps explain where I'm coming from: I never studied for any of my high school exams (and also not a lot for the uni exams) but I was still very good at them. Everyone always told me how impressive that was and that I must be proud but internally I was just like "What? I didn't do anything!". That everyone else thought getting good grades was "hard" didn't result in a lot of internal validation on my end.

But maybe that explains more about ways in which I am abnormal than about humans in general :P

Relativisticcucumber

@ACuriousMind that's interesting bc i think i am the opposite. i think i generally have to work harder than others, so i admire the people who have natural skill and i think highly of that raw ability.

i mean i was not really given pat on the backs in my life for trying. the pat on the backs were given for if i could do smth or not, not how hard i tried compared to others

and after a decade of sadness i accepted this fact of life xD

and life has been easier for me ever since

think_meaning_buildß

this is heading towards "mindset"

Silly Goose

@Relativisticcucumber well i think life pats on the back people with raw ability who also work harder than others

Relativisticcucumber

20:21

@SillyGoose well yes, that is what we call OP

Herr Feinmann

I think qmechanic likes me, they gave me this "OP" nickname. How do you guys know that?

Relativisticcucumber

@HerrFeinmann huh?

ACuriousMind

@Relativisticcucumber well, but we were talking about an internal feeling of validation, not others patting us on the back - I agree society generally will not care how hard you try at anything

Relativisticcucumber

OH

Herr Feinmann

@Relativisticcucumber Failed joke

Relativisticcucumber

20:23

original poster

Herr Feinmann

@Relativisticcucumber OH

Relativisticcucumber

no no i got it. just late. it's the greater effort required time lag

Silly Goose

society wants answers!

Relativisticcucumber

@ACuriousMind yeah but i guess it's hard to not have one's internal schematic be influenced by society

think_meaning_buildß

but only you know how hard you tried

Relativisticcucumber

20:24

i mean i try but xD

@think_meaning_buildß yes and it just makes me sad so i try not to think ab it xD

Herr Feinmann

@ACuriousMind never studied or didn't study as much as the average person?

You are built different, my guy :P

ACuriousMind

@Relativisticcucumber impossible, even - but I think we should try and be reflective about which of the ideas we've internalized we could maybe do without

think_meaning_buildß

learn from your mistakes as well as your successes

ACuriousMind

@HerrFeinmann Never in school, really, and typically only the 1 or 2 days before the exam in uni. I did do most of the homework/exercises from the lessons/courses, though, but others do not seem to count that under "studying for the exam" :P

Herr Feinmann

Then when did you learn all of the things you know about gauge theory and stuff like that? :P

Relativisticcucumber

20:27

@HerrFeinmann that 1-2 days

Herr Feinmann

LOL

ACuriousMind

@HerrFeinmann I'm not sure how that relates to not studying a lot for the exams - e.g. almost all the gauge theory stuff I learned when writing my Bachelor's thesis about 2d gauge theories, that was a lot of studying, but not for an exam of a course. I've also never needed to do e.g. all the formal QM functional analysis stuff in an exam, I just learned that for fun (presumably in the time when others were studying for their exams :P)

Herr Feinmann

Oh, I see. I used to have this method during my bachelor. I would mainly study things that were interesting for me and then realized that the superposition with the courses was such that I barely needed to review the program

But that only happened for a few good courses and with an efficiency incomparable to yours, just I suppose it is the same mechanism

think_meaning_buildß

you people are ahead of the curve

Herr Feinmann

I'm more of a big head and my knowledge is far from impressive. ACM is definitely in the tail of the curve

Relativisticcucumber

20:36

@think_meaning_buildß so ahead of the curve, the curve became a sphere

Silly Goose

are there internal higher order magnetic moments?

spin <-> magnetic dipole
? <-> magnetic quadrupole
etc.

think_meaning_buildß

@Relativisticcucumber yup

ACuriousMind

@SillyGoose see physics.stackexchange.com/a/119802/50583 - spin-1 particles can have quadrupole moments, spin-1/2s can't

it's not really that spin corresponds explicitly to dipole, but that by Wigner-Eckart spin-1/2 particles only have the dipole moment, so you often see this association, but really the higher moments just mean higher spin, not some new spin-like thing

think_meaning_buildß

21:07

@Relativisticcucumber like asking what time is it at the north or south pole :P

Silly Goose

21:51

I do not know how anyone can honestly say that Ashcroft & Mermin's exposition of electrons in a weak periodic potential is good.

Tobias Fünke

23:10

@SillyGoose cmon

I tried to follow the discussion...but it was hard for me right now.

To start, I think the problem is language; at least this is what my takeaway was when I left. You seem to be unhappy about the wording "free electron gas" or so (?)

section 17.2.1 in "Fundamentals of the Physics of Solids Volume II: Electronic Properties" might help (and it should to a large extent be available via Google Books)

Silly Goose

@TobiasFünke okay let me take a look at this

Tobias Fünke

23:30

My two (additional) cents. You start with Bloch's theorem (say, 1D lattice $L=Na$). You see that you can write the eigenfunctions of the (lattice) periodic Hamiltonian as Bloch functions, which are indexed by $k$ and $n$, where the former obeys the BvK boundary conditions. You further see that you only need $k$ from the 1BZ. Let's do so; you end up with $E_n(k)$ and $\psi_{nk}$ and have the "usual" band structure. Fine so far?

Now sometimes it seems convenient to extend the *definition* or *construction* of these entities to $k$ not only from the 1BZ. One obvious thing to do is to say that…

I haven't checked the one screenshot you posted from the book you study, but I'd guess that they did exactly this for the free electron gas, i.e. no lattice potential (but a lattice structure).

It is really late, so I hope I did not do a mistake here, but that's essentially it. It should be explained somewhere in some book properly, but I don't know by heart right now.

Allie

23:51

meow

Tobias Fünke

or well, they seem to made the reverse: starting from the solution $E(k)=k^2/2$ for all $k$ obeying BvK bc, they defined within the 1BZ all bands. I don't know why they did it, but it should also answer your question. They started from "one band" in the extended zone scheme (all $k$ points) to and ended up with infinite bands in the reduced zone scheme ($k$ only from the 1BZ).

hey Allie.

I g2g to bed now, see you!

Allie

awwww

dang time zones

Silly Goose

Am I missing something? This table on wikipedia suggests that the electrical resistivity does not "hardly increase" with increasing atomic number.

Allie

idk it doesnt seem to drastically increase to me

Transcript for