The h Bar

Silly Goose

00:04

hm i see

Relativisticcucumber

00:57

in my condensed matter class, we encounter this notion of "nearly degenerate". i only recall there being degenerate or not degenerate. i thought we deal with degenerate perturbation theory separately (from reg pert theory) because the energy differences occur in the denominator, and this becomes problematic when energies are degenerate. if they are just nearly degenerate, this isnt a problem since the difference wont be zero, so what's going on with this notion of "near degeneracy"

Silly Goose

01:21

Is this a sort of heuristic for Laurent vs. Taylor series?

here $f(z)$ is holomorphic within the outer dashed circle with the exception of singularities $z_1, z_2$. The shaded blobs visualize where the Laurent and Taylor series of $f(z)$ converge, respectively.

123

03:02

Hello Everyone...

PM 2Ring

That tachyon question got closed. Again. Ok, I get why some people think it's not suitable for the site, but closing it as homework-like is ridiculous!

2

Q: If we imagine tachyonic particles do exist, then can they travel slower than the speed of light $c$ from a reference frame traveling slower than $c$?

If we imagine a tachyonic particle travelling faster than the speed of light, can there be any reference frame which perceives a tachyon as travelling slower than $c$ by applying Lorentz contraction? Also, can a tachyon perceive a tachyon to be travelling faster than $c$? (I imagine that tachyon ...

@SillyGoose Your sketch reminds me of a binary orbit diagram I did the other day.

Here's an example with eccentricity 1/3 & mass ratio 1:2 where the orbits just touch. i.sstatic.net/4avXdzqL.png — PM 2Ring 2 days ago

Sorry, that has nothing to do with your question about Taylor & Laurent series. Just going off on a tangent...

naturallyInconsistent

03:30

@Relativisticcucumber If you have a near degeneracy, it is not as bad as exact degeneracy as you correctly noted, but it is still a small denominator, and on top of that, you cannot know in advance if the perturbation causes the states to cross in energy. The only perturbation theory that you know might be Rayleigh-Schrödinger, but if you look up Brillouin-Wigner, you will see that the RS perturbation is doomed to diverge if you see that, in BW perturbation, the energy levels cross.

So, you kind of have to diagonalise the Hamiltonian within an energy band that is widely separated from the rest, in order to make sure that things don't blow up in your face. Of course, if you are smart about things, you can make do without such a thing, but that always requires physical insight, which is a tremendously scarce resource. We tend to want to have naïve implementations of stuff just give us correct answers, even if the price is just a bit more computation.

qwerty

03:54

@PM2Ring do only mods close questions?

PM 2Ring

04:05

@qwerty No. Ordinary members with 3000+ rep can vote to close, or to re-open. On Physics.SE, it takes 3 votes to close or open a question. (On most sites, it takes 5 votes). Mods can close or open single-handedly.

See physics.stackexchange.com/help/privileges/close-questions for details

Lucky Chouhan

04:31

@qwerty I really feel sorry for you, so when you discovered your interest in physics. I'm asking because I think you discovered it late in your college, if you had discovered it in your high school or before that then you would have chosen better university. (?)

@qwerty So you're doing your PhD these days? Yeah, it is really discouraging not being able to do what you want to do. Do you feel discouraged when you can't solve a physics problem which you're supposed to solve? I know that to solve some problems we're supposed to know some stuff which is required to solve that and, in the case, where we don't know then......

@qwerty nice, so what was your thesis?

qwerty

06:15

@LuckyChouhan no, I went to a good university. I finished my PhD a while ago. I bring all this up in this forum as I strongly believe this is a very much a systemic issue in academia, at a range of institutions including the best ones; it's not an individual issue.

for example nature.com/articles/d41586-018-05634-8

that's a top institute in the world.

buzzfeednews.com/article/pascalemueller/…

back when BuzzFeed news was doing investigative journalism. it broke this story and it was huge

@LuckyChouhan no I don't. you misunderstand what I mean - I was talking about PTSD symptoms.

Ryder Rude

in total recall, if it is a dream, the company could hav easily convinced him it was a dream by bringing back any one of the people who died

but they choose to bring his wife along with the doctor to convince him, which means either they're dumb or it is not a dream

qwerty

@LuckyChouhan here's another article on this matter. nature.com/articles/d41586-021-02024-5

and another sciencedirect.com/science/article/pii/S2589537021004016

> An overwhelming proportion of participants reported either experiencing (84%) or witnessing (59%) abusive supervision, or both (49%).

Ryder Rude

@PM2Ring this is ridiculous indeed. they could've called it "non mainstream", but even that doesnt apply

Lucky Chouhan

06:41

@qwerty How much time did it take you to complete your PhD thesis? Would you share its link?

I didn't know about this issue where some researchers are bullying junior researchers, it is very concerning.

@qwerty Yeah, PTSD I see. I just got to know to know about it.

qwerty

@LuckyChouhan sorry I'm already at about the limit of personal info I'm comfortable sharing. what I did share is kind of just to talk about the problems in academia

Lucky Chouhan

@qwerty okay, as you have a phd, so would you please tell me how many hours did you used to spend every day working on it?

qwerty

07:00

that's a very complicated thing to answer. results don't correlate with hours

it's not like undergraduate

plus people change projects, are asked to do other tasks. some projects are dead ends even in the best of circumstances. some people teach, some people take coursework.

123

07:55

What is the purpose and role of observer in Newtonian mechanics, SR, GR and QM?

Slereah

they observe

Typically they define a frame

123

Hi @Slereah

observe means to say. What if i set coordinate system to the frame e.g. bus and i am observer inside the bus. Is it also possible?

If human is an observer we are limited to observe parameters from our 5 senses. And these senses are not very accurate and universal for light, sound, pressure , stress and temperature.

123

08:24

Hi @RyderRude

Ryder Rude

@123 hi

123

Can you pls clear me the confusion about observer role and relation with frame of reference and coordinate system

Ryder Rude

an observer in classical mechanics is a co ordinate system on spacetime

it's just a description of events wrt a co ordinate system

nothing to do with humans senses

123

@RyderRude Aaaah... Okay...

Ryder Rude

u have have seen Galilean/ Lorentz co ordinate axes. that is a good way to get an idea of an observer

123

08:35

@RyderRude Yes... observer means a coordinate system attached to it?

Ryder Rude

@123 yes

123

What is meant by frame in classical mechanics and SR?

Ryder Rude

it is a co ordinate system

123

@RyderRude What i think frame is like a box at which we have a choice to select reference to observe phenomenon. e.g. we have laboratory frame, bus moving in a straight line with constant velocity and airplane flying. All three things are frame. If i select a bus from all three, then bus is a frame of reference. Am i correct?

Ryder Rude

@123 a frame of reference associated to an object is a co ordinate system in which that object is at rest. e.g. the frame of reference of an airplane is the co ordinate system where that airplane is at rest

123

08:41

And if all three are inertial frames, then bus is called inertial frame of reference , it is physical and we attach coordinate system to it.

Ryder Rude

@123 yes

123

@RyderRude Which object is at rest? The object or system under consideration is at rest?

Ryder Rude

@123 i said object... e.g. the airplane

ACuriousMind

@123 Why do you act as if you don't know what a frame is? You've been using the word for 4 years and now you ask this question as if you encountered the word for the first time?

123

Can we discuss this in that chat room?

ACuriousMind

08:46

This is an useless way to start a conversation. If you have something specific you want to ask about frames, ask that. But asking "What is a frame?" without any additional information when you've been talking about things in different frames for years here is close to trolling.

123

ACM i remember that discussion. But there is still confusion. So i need to finalize the concept. Sorry if this discussion bother you.

Ryder Rude

@123 i don't think there is too much to discuss here. u seem to have the right idea..

but let's discuss, sure :)

ACuriousMind

@123 You remember which discussion? I linked a search result showing all your usages of "frame", not a specific discussion? My point is if you need to "finalize the concept", whatever that means, you should be able to ask a more specific question than "what is a frame"

123

ACM still i have a wrong concept about frame of reference. So i need to flush incorrect things. I taught frame can be use separately like bus, airplane etc... These all are frame. But as you said frame word itself has no meaning. This information is useful for me.

Ryder Rude

@123 as a side note, i think a lot of questions u ask are really supposed to be learned from books.. Books explain this really well :)

2

ACuriousMind

08:50

Asking such general questions when you already know the basic concept is just a waste of time for people who try to answer the general question. Please be more respectful of the time people potentially spend on your questions here and be as specific as possible.

Ryder Rude

chat is for smaller questions, like specific ones u didn't understand from the book

ACuriousMind

And, once again, if you still don't know the basics of what a frame is after 4 years of talking about it, asking questions in this chat is clearly not working for you.

123

Yes i am specific to the questions. Just need to clear the understanding. That's why i asked to discuss in different chat. I don't want to bother anyone. Everyone is respectful for me.

ACM... Pls don't underestimate me. This is not the case.

Ryder Rude

@123 ACuriousMind is only criticising ur approach, not ur abilities :)

and this is constructive criticism. i think u must take feedback

qwerty

@123 As I have said to you before. Spend some time to think through things before you ask. I know you are not doing this because of the frequency at which you are asking things in the chat.

You should have more faith in yourself to work things out by yourself.

123

08:55

@RyderRude You are right. I am taking ACM discussion positively.

@qwerty I never asked anything as i learned newly. I always spend a lot of time and days or months or more with the topic, and try to learn from internet and other books, if still not clear. Then i asked to people who has real information about the topic means here.

Ryder Rude

u have to try what qwerty suggests. about this particular question, u already have the right idea what a frame of reference is. if, instead of asking what a frame of reference is (which is in a book in a much more detailed way than anything i say), u can ask if u think theres something wrong with the book discussion

ACuriousMind

@123 If you don't want me to underestimate you, you need to show some more actual effort. Instead of asking "What is a frame?" as if you are a beginner, present more detail. Show your current understanding of the term, and what made you unsure about it so that you felt the need to ask that question. You said you need to "finalize the concept", that means you already need to have a basic understanding of the concept, and some specific aspects you want to clarify.

None of this is evident from the extremely basic questions you're asking.

qwerty

RR is right. You should have the ability by now to find the information you're seeking in books and to piece it together.

I do not believe you are doing this.

Maybe you're not finding the right books, maybe you're not thinking on it long enough. If you were doing any of what I have been repeatedly suggesting to you, you would find it much easier to do what ACM is telling you and be able to be much more specific.

123

@qwerty This is no the case. Basically all of you have extra edge English is your mother tongue. Furthermore you all have good teachers in your school and university. This is not in my case.

ACuriousMind

English is not my mother tongue.

qwerty

09:02

Then spend more time learning English, as had already been suggested to you!

123

I need to put 4 times effort try to understand what books is saying. And i don't want to go with wrong concepts.

Ryder Rude

@123 we understand those problems :) we r just saying that a good template for asking questions would be : "i read this discussion in the book. this is what I understand. this is what i don't understand"

a lot of other people ask questions here with that template @123

qwerty

@123 the English in the books will be clearer and more precise than whatever anyone types to you here!!

123

Okay... I will work on it. But none of the book have completely cover the topic. But i will try to be more specific.

Ryder Rude

exactly. "What is a frame reference" is something that is in the books in an extremely clearer way than anything i say here

123

09:06

@ACuriousMind You are right. I must follow your instructions, if sometime i will do mistake then pls ignore. I just want to clear the concept. Thanks for your constructive input.

Slereah

@123 Do they not have physics books in your land

123

I have more than 100 books just for classical mechanics in my laptop. We have physics books here

Ryder Rude

09:43

Is Quantum Mechanics or General Relativity More Fundamental?

►

naturallyInconsistent

@qwerty hugs that is one kind of articles that should not be behind a paywall.

Ryder Rude

The 1st Ockham Debate - The Problem of Quantum Measurement - 13th May 2013

►

qwerty

@naturallyInconsistent hugs. Definitely.

Ryder Rude

09:59

Kastner is extremely critical of other interpretations of QM transactionalinterpretation.org

i also got to know something about the Copenhagen interpretation. Apparently, the objective collapse and classical-quantum divide stuff seems to be from the early days of Copenhagen interpretation

in the later days, Heisenberg thought that this process was non local, and starting promoting a "subjective collapse" idea in the name of Copenhagen interpretation

i.e. the collapse is not a physical process, but the update of knowledge of an agent.. and that no one should talk about what exists objectively

the wiki article expresses both these viewpoints en.m.wikipedia.org/wiki/Copenhagen_interpretation

but this means that Copenhagen interpretation is contradictory ideas going by the same name

i wonder if Bohr also revised his viewpoint and still kept calling it Copenhagen interpretation

naturallyInconsistent

@qwerty it is also why quite many of us respect profs who never get angry. Emotional control is way too underrated.

qwerty

10:16

@naturallyInconsistent that's true, but I think academia is a hothouse for this sort of behaviour in a very structural way. you basically have these little fiefdoms with very limited external oversight. in my country, you're not employees so you don't even have workplace recognition or protection.

I'd like to see things change - for example I heard Cambridge does not permit 1:1 advisee-student relationships (they have panels) which I think can help, if only academics took it seriously at all. In my experience many of them thought of it as a tick box exercise or bureaucratic nonsense.

"publish or perish" doesn't help either. people think that the replication crisis is limited to the soft sciences, but it isn't.

to be honest, I think that individual emotional control or personality seems like it might be a cause. but it's the system that allows individuals to perpetuate their behaviour without consequence.

Ryder Rude

10:39

what r some bizarre horror movies like Re Animator

also, i didn't like From Beyond that much. 5/10

123

I am carefully reading, Is laboratory frame along the surface of the Earth is an inertial frame approximately.

I found one answer where one says. It depend on the experiment type. My question about one sentence where he emphasized about experiments on slow speed and small distance.

My question is, To make good approximation of lab frame on SoE is inertial, experiment should be slow speed and with smaller distance?

I asked this question , because he didn't clear that point.

For example i am doing experiment of law of conservation of linear momentum on linear air track.

qwerty

11:07

@123 when did you read this passage?

123

Today. I asked just because there were no explanation of this. Otherwise i didn't aske here.

qwerty

you should not be asking within the same day. I also dont understand what's unclear about the text at all.

NOTE Book

hi

123

If my experiment is following the prescription of slow speed and small distances e.g. experiment of law of conservation of linear momentum on linear air track. Then surface of the Earth will be a good approximation as inertial frame?

NOTE Book

Since conservative forces are those forces whose work is independent of path can we also say that if for a force work done on any 2 different path is same it should be conservative?

naturallyInconsistent

11:27

@123 how was the answer worded, exactly?

@NOTEBook just 2 of them? could be a fluke. Otherwise, prove the set of 4.

123

@naturallyInconsistent qr.ae/p2awwk Pls see link at the last paragraph.

ACuriousMind

You linked an answer that ends with "There is more to it than just getting an answer from someone on the internet then moving to the next question.". Very fitting.

2

naturallyInconsistent

@123 this answer is correct. What part of it is so unclear that you cannot answer your own question?

123

@naturallyInconsistent Problem in last paragraph. What he is trying to say about slow speed over small distances.

NOTE Book

@naturallyInconsistent So it is possible that 2 paths of non conservative force can have same work done if initial and final position are same?

qwerty

11:34

@123 You read this today. why don't you think about it for at least a week. You have 100 physics books on classical mechanics and you have the whole internet. this is not a high level technical problem. you can figure this out yourself.

naturallyInconsistent

@NOTEBook yes, by fluke. you usually can find different paths having the same work done

@123 I think that is extremely clear. What part of that is unclear? Why do you need to ask us this question?

NOTE Book

oh ok thanks

123

Ookay my friend..

NOTE Book

11:49

@naturallyInconsistent hi

naturallyInconsistent

hi

NOTE Book

Can you help me understand potential energy

Like when we say an object has mgh PE

Does it mean that at this state if block is released then gravity will do work on object due to which its final KE will be mgh?

naturallyInconsistent

if the complete amount of GPE is converted to KE, yes

NOTE Book

Or is it like block already has energy like phones battery?

Yes I am only talking for ideal conditions right now

naturallyInconsistent

they already have energy, but the parts staying constant is of no use to consider, for now

Ryder Rude

12:24

youtu.be/NKPI_wurNlo?si=uKdMizQ3JQTZRmbO this debate is a massive misunderstanding of QM

"when u r in a room with a many worlder u have the worse understanding of QM"

i cant believe no one called out the second guy

and the second guy is the physicist of the two. the many worlder is a philosopher

the second guy believes that we can recover non determinism of QM using deterministic dynamics of wavefunction + ignorance

the argument he has is "Occam's razor"

123

13:40

Why objects resistance against change in its state termed as mass? In my view because before atom and subatomic particle discovery quantity of matter considered as mass. And objects resistance against change in its state directly related to quantity and type of material. It is better way of operationally define mass than before atom discovery. Am i correct?

Ryder Rude

14:00

@123 the quantity of matter definition does not always work. suppose u have an electron and proton. how do u compare their masses if u define mass to be "quantity of matter"? the quantity of matter thing can only help u define mass when all particles are of the same type. e.g. if there were only electrons in the universe, then u could define mass of 1 electron as 1 unit and that of k electrons as k units

the resistance to motion definition is more general. it helps u compare the masses of electron and proton. and it agrees with the "quantity of matter" definition where quantity of matter can be defined, at least non relativistically

Relativisticcucumber

ive got to say i really dont understand the widespread appeal of david tongs notes

the man does lattices AFTER tight binding and band structure

????? just how

ACuriousMind

@123 Why are you just quoting the second sentence of the Wikipedia article on mass?

> It was traditionally believed to be related to the quantity of matter in a body, until the discovery of the atom and particle physics.

That's literally what you just said. What is the question?

Slereah

> The term Mass is commonly used in the Catholic Church,[1] Western Rite Orthodoxy, Old Catholicism, and Independent Catholicism.

Not sure I agree!

ACuriousMind

I linked the correct article, not the liturgy one :P

Slereah

Are you accusing me of going to the wrong article on purpose

ACuriousMind

14:13

yes :O

Slereah

Damn he got me

qwerty

Ite, missa est

@Relativisticcucumber I liked dipping in and out of them during undergrad. they seemed comprehensive and detailed

Ryder Rude

@Slereah hi. what r some movies like Re Animator

i also saw Total recall

i got this movie called return of the Living dead

Slereah

14:38

I'm not sure there are any movies like Re Animator

Ryder Rude

15:01

makes sense :P

i give total recall 8/10

Slereah

which one

Ryder Rude

there are multiples?

i saw the one with Arnold

there seems to be a remake

123

@RyderRude thanks. It means my thinking is correct. Because quantity of matter better relates resistance against motion change. That's why we called it mass.

@ACuriousMind basically I used that idea of mass from wiki traditionally. My question was why resistance against motion also termed as mass , we can give it other name. I think there are special reasons we give name mass of resistance against motion, because it is always constant independent of external factor. Second it is directly increase with increase in matter etc.

also it is better way to explain mass indirectly than traditionally. It depends on types of material means no of proton , neutron and electron in material except directly quantity of matter. ACM am I correct?

PM 2Ring

@RyderRude How about Teenage Mutant Ninja Turtle Recall? ;)

Slereah

I would not recommend the remake

Possibly one of the worst movie of all times

Ryder Rude

15:18

@PM2Ring what is this :P

@Slereah lol

I'm not sure I can show re animator to anyone else. it has some extremely disturbing content

Slereah

The bad guy does look lile John Kerry a lot

Quite disturbing

Ryder Rude

lol

yes, they look similar

also, the science obsessed guy seems like a grey character. i initially thought he was the main bad guy

West

Slereah

Would have preferred a movie more like the original story really

The ending is so silly in that story

Ryder Rude

oh. what was the original ending

the science obsessed guy wanted to do the experiment any chance he got xD

even when facing death

Slereah

The original story is quite different from the book

Longer in scope

Ryder Rude

15:27

oh

so there r three versions

Story, book, movie

Slereah

The story is the book :p

Herbert West just spends a whole story making spooky monsters and in the end they come for him

Ryder Rude

oh. this is a completely different story from the movie

Slereah

> There was no sound, but just then the electric lights went out and I saw outlined against some phosphorescence of the nether world a horde of silent toiling things which only insanity—or worse—could create. Their outlines were human, semi-human, fractionally human, and not human at all—the horde was grotesquely heterogeneous.
They were removing the stones quietly, one by one, from the centuried wall. And then, as the breach became large enough, they came out into the laboratory in single file; led by a stalking thing with a beautiful head made of wax. A sort of mad-eyed monstrosity behind…

There's a scene I want to see in a visual media

Ryder Rude

wow...

maybe they didn't like being undead

in total recall, if it was not real, the company could've convinced Arnold by bringing back someone whom Arnold had seen dying, like his co worker

but they didn't think of that, which is odd. so maybe total recall is all real

PM 2Ring

15:45

@RyderRude Many of Phillip K. Dick's stories involve mutable reality. In some ways, it's a bit easier to present that kind of thing in a movie, it's a bit more subtle in written form. One of the more intense examples is Ubik. en.wikipedia.org/wiki/Ubik

Ryder Rude

@PM2Ring oh. i also thought total recall was intentionally ambiguous

@PM2Ring there is a movie called vanilla sky based on this death hibernation idea

all these movies are soo similar

too many movies based on questioning ur reality and ambiguous stuff

PM 2Ring

Guys like P. K. Dick were writing about it 20 or 30 years before they started making movies on the theme.

Ryder Rude

oh

I wonder if these ideas existed 1000 years ago

Descartes questioned his reality in 1600s but he was doing philosophy

maybe they made their entry in fiction later

Slereah

Plato's cave

PM 2Ring

Imagine trying to make a movie like Inception in the 1960s. It would have been difficult without digital special effects. And most of the audience would be baffled. The books were necessary to introduce the ideas.

Slereah

15:54

Or the classic

Zhuangzi (book)

The Zhuangzi (historically romanized Chuang Tzŭ) is an ancient Chinese text that is one of the two foundational texts of Taoism, alongside the Tao Te Ching. It was written during the late Warring States period (476–221 BC) and is named for its traditional author, Zhuang Zhou, who is customarily known as "Zhuangzi" ("Master Zhuang"). The Zhuangzi consists of stories and maxims that exemplify the nature of the ideal Taoist sage. It contains numerous anecdotes, allegories, parables, and fables, often expressed with irreverence or humor. Recurring themes include embracing spontaneity and achieving...

@PM2Ring have you never seen the twilight zone

They did that all the time

Hell the Wizard of Oz was that plot

PM 2Ring

@RyderRude Fair point. Descartes mostly focused on a benevolent God. But he did also discuss the concept of a demon presenting total BS to you.

@Slereah Not to the same degree as P. K. Dick, and with multiple layers.

Ryder Rude

@Slereah this idea does question reality, yes

@PM2Ring yes

PM 2Ring

But sure reality / illusion goes back to ancient times. Eg, the whole Hindu doctrine of maya.

Ryder Rude

I think Descartes was into the "maybe it is all a dream" philosophy

Slereah

@PM2Ring Is the issue quantity

Ryder Rude

15:59

@PM2Ring Inception is also a very original take on this idea. it adds a lot of structure to the dream world

@PM2Ring oh

Slereah

People of the early 20th century were very familiar with weird ideas if they were interested in the topic

It was a pretty loadbearing section of the counter culture

PM 2Ring

Not just quantity. Complexity. In a simple story, you have a real world and a dream world. But it gets tricky when there are multiple layers, and no way to tell which layer you're in. At the start of Inception, they do stuff to keep track of that, but it gradually falls apart.

Slereah

I don't think that is particularly complex

Ryder Rude

the more layers u add, the more bizarre the story gets. people lose track of reality. This is an element in many of these stories

Slereah

also the theme of Dark Star in the 60's btw

Dark Star - Talking to the bomb

►

PM 2Ring

16:05

You can't get too complex in a movie, or you lose too much of your audience. IMHO, Inception does a pretty good job. But it's pretty tame compared to Ubik.

Slereah

Also really, once you go beyond two layers, it's pretty diminishing returns :p

Ever saw that Rick and Morty episode

PM 2Ring

@Slereah You mean stuff like theosophy?

Slereah

@PM2Ring I mean that's part of it I guess?

But also like surrealism

PM 2Ring

Ok

Slereah

Rick and Morty You're are a decoy clip

►

After too many layers of twists it loses its novelty

The 60's was full of weird reality bending media rly but people do not remember it because everyone wore unfashionable turtlenecks

Family Guy - The end of a depressing 1970s sci-fi movie starring a guy in a turtle neck

►

it's turtlenecks all the way down

Theosophy, and all the way down Gauss, is the source for a staple of cheap modern scifi btw

The notion of a ~plane~

different plane of existence

imbAF

21:01

When considering a system of two electrons, why an arbitrary state is written as : $\psi=\alpha|+,-\rangle + \beta|-,+\rangle$? Why aren't $|+,+\rangle$ and $|-,-\rangle$ used?

Slereah

It is also a possibility?

Where are you seeing that expression

It may be irreps related

Silly Goose

What is a clean way to understand how to integrate $\int_0^\infty e^{-it\omega}$?

The derivations I have seen either (1) require what seems like a year of complex and functional analysis to understand or (2) use some arbitrary manipulations and limiting procedures.

imbAF

@Slereah I am considering a setup of two electrons. And we are describing what the basis is, which are the four combinations of the Z-component of spin

Then it is said that a phys. State is described as $\psi=\alpha|+,-\rangle + \beta|-,+\rangle$ $\rightarrow$ "Exchange degeneracy"

Slereah

It's common to decompose tensor products of spinors into their irreps

imbAF

irreps?

Slereah

21:14

Irreducible representations

Basically you can consider it as a system made of a spin 0 particle and a spin one particle

imbAF

Hmm.. but what about $|+,+\rangle$ and $|-,-\rangle$

isn't that spin 1?

Slereah

Those are the spin 1 part yes

imbAF

I am just confused, because since the basis includes all four, then an arbitrary state should be a linear comb. of all four

And not just two only

Slereah

Sure

imbAF

But what I find more odd is the example given in this context

Mr. Feynman

21:19

@SillyGoose so you don't want rigorous answer but sloppy manipulations are not fine :P

Also, functional analysis? That being said, the manipulations are arbitrary because you are giving a meaning to an integral that wouldn't ordinarily have one

imbAF

@Slereah
We want to find the prob. that the x-components of the spins, of both particles, are $+\hbar/2$. So the following is done:
$P(S_{1x}=\frac{\hbar}{2},S_{2x}=\frac{\hbar}{2})=|(\frac{1}{2}\langle +,+|+\langle -,+|+\langle -,-|,\langle +,-|)(\alpha|+,-\rangle)+\beta|-,+\rangle|^2$

I know, in the simple case when you have some State, expressed as a linear combination of eigenstates of some op. the probability of measuring the arbitrary eigenvalue $n$ would be $P(n)=|\langle n |\psi\rangle|^2$

And the same logic should apply in the example given. But since when does an eigenstate of the system looks like that ?

Silly Goose

22:47

@Mr.Feynman It seems like to rigorously do the integral, one needs to do distribution theory which requires knowing how to define distributions in terms of their action on nice function spaces

well i was hoping there was some reasonable explanation for the integral that was not entirely rigorous :P

Silly Goose

23:12

I don't understand where the $e^{i(m_\phi - E_\chi - E_\psi)t}$ term goes in the $\Delta E_\phi$ term. I can reason that it disappears by property of the delta distribution in the $\Gamma$ term, but I cannot reason why it can disappear in the $\Delta E_\phi$ term.

Relativisticcucumber

23:34

@naturallyInconsistent i have a follow up to the answer you provide here. in the figure, theres a region where s and p kind of open up into each other. what i mean is theres an $a$ where there is no band gap. is this hybridization?

1

A: How to conceptually understand bands in a solid?

I really think this is one of those things that really should not be done as an afterthought, as Tong is doing. You should be picking up a proper condensed matter / solid state physics text and learning step-by-step what is being meant. The central idea that is not proved but is experimentally ob...

Silly Goose

23:44

here is what I gathered the calculation in detail should kind of look like

So in particular, I am not understanding what happens to the $\lim_{t \to \infty} e^{-i\omega t}$ in the final line. Seemingly, it disappears in the paper I screenshotted.

Er $e^{-i\omega t}$ should be $e^{i\omega t}$

Transcript for