Bose-Einstein Condensate: The Quantum BASICS - Bosons and their Wave Functions (Physics by Parth G)
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- Опубликовано: 22 июл 2024
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A Bose-Einstein Condensate (BEC) is often said to be a "fifth state of matter". But what exactly is it? In this video, I wanted to discuss BECs and the basic mathematical descriptions derived from the theory of quantum mechanics. #boseeinsteincondensate #quantumphysics #BEC
Firstly, we need to consider certain particles known as Bosons. (Both Bosons and the Bose-Einstein condensate are named after Indian Physicist Satyendra Nath Bose). Now as it turns out, Bosons are a class of "indistinguishable" particle. This means that if we have a system of two or more bosons, all we can know is the number of bosons in our system. They are identical to each other in every way (same mass, same charge, etc). And if we label each particle in the system and then leave the system to evolve, then some time later we have absolutely no way of knowing which particle is which.
In order for this to be actually true in our universe, and not just some mathematical fantasy, the wave functions of our systems need to behave in a specific way. A wave function contains all the mathematical information we can have about our system. And the square modulus of the wave function is directly related to the probability of certain getting certain experimental results on our system (such as finding our particles at given points in space). If the particles really are indistinguishable, then the square modulus of the wave function must be exactly the same regardless of what orientation we have our labelled particles in - thereby rendering the labelling of our particles incorrect.
So if the square modulus of the wave function must be identical under particle exchange, then the wave function itself must behave in such a way that it either remains the same under particle exchange, or it becomes negative. The first of these two possibilities is referred to as a "symmetric" wave function, and the second is "antisymmetric". Any kind of particle with a symmetric wave function is called a "boson", and any kind with an antisymmetric wave function is called a "fermion". The focus here is on bosons of course.
When constructing a wave function for a boson system, we find that it is possible for two (or more) bosons to be in the same energy level (or state) and still result in an overall symmetric wave function. This is different to fermions, for which there is no way to construct an antisymmetric wave function while allowing two or more particles to be in the same energy level. This can be thought of as a very important difference between bosons and fermions.
And as it turns out, the ability of bosons to all occupy the same energy level, is what allows Bose-Einstein Condensation to occur. A BEC is formed when a boson gas of relatively low density is cooled below a certain critical temperature. This critical temperature depends on the density of the bosons and the mass of the bosons. Once below this critical temperature, all of the bosons fall into the lowest energy state and often can even occupy a very very small region of space.
BECs are interesting because they clearly display quantum behaviour that would otherwise be restricted to the very small scale. For example, superfluidity (en.wikipedia.org/wiki/Superfl...) has been observed in BECs. It's important to note that these quantum behaviours are not direct consequences of the BEC, but are easily observed in one.
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Hello! I love your explanation. Could you please make a video on Young’s Modulus too ?I will be ever so grateful!🤍 Thank you 🤓
But i dont understand what is so special in - all particles being in the same state (energy state)?
SN Bose was probably major figure in science who is very much underrated and goes unappreciated.
Yup…:)
Trueeeeeeeeee
So glad his name was given to the class of particles. Hopefully, that will help future generations remove the blinders.
Exactly
@@matthewhoag2609 👍
Masterful explanation Parth! Great introduction to some of the math that leads to the Pauli exclusion principle. I think viewers of my recent video on superconductivity will find this video super helpful. Perfect blending of math and intuition.
Wow u are here!
Thanks so much Arvin! :D
how we know that mass and charge of an electron is always constant to another electron? Plz answer
I just came here after watching your video about superconductivity 😂✌🏻
no one
literally no one
parth and arvin commenting on each others videos
A priest, a Higgs boson and a neutrino walk into a bar. The bartender asks “what you guys do for a living?” The Priest and the Higgs say ”I give mass.” The neutrino says “That’s not my field.”
Neutrinos do have some mass though.
@@erdemmemisyazici3950 maybe. I'm more interested in whether Majorana or Dirac was right. I lean toward Majorana simply because he had a cooler sounding name.
AHAHAHA
@@erdemmemisyazici3950 but it isn't the higgs mechanism that gives them mass (at least not the most simple one used for charged fermions), so the joke still works.
Wow that was so funny
The best illustrated explanation that I needed for quite some time now.
Just recently discovered your channel and I must say it is amazing. Thank you for providing such great quality content!
How have I never seen this channel before???!!? Lord you've got so many lists explaining very hard concepts easily... Thank you for all of this
Funnily enough this helped me greatly in getting a better intuition for the Pauli exclusion principle. Thanks a lot!!
Thank You very much! This is the best video on BEC I have seen yet. No fancy general blah blah blah, but talk and graphics right into the core concepts. I subscribed Your channel.
There’s a saying that goes, “if you can’t explain it simply, you simply do not understand it enough.” Or something like that.
This man here; Understands more than enough. Awesome video!
Definitely enjoyed this video - excellent theoretical and application of BEC descriptions.
I'm gonna be doing my master's dissertation on BECs so I definitely will be binging your videos along with others. Thanks :)
I am amazed by the explanation.
This video leads to open new horizon in my understanding on Bose-Einstein Condensation.
Thanks for the sharing.
Finally a video I've been waiting for months😀😀🔥🔥
Amazing video dude. Keep it up.
Wow 100k, congratulations
To 1M and beyond
Loved it your explanation is so good!! Gonna watch all your videos. Really really helpful🤩👍
Excellent video Parth! Love your channel
Exceptional video, as always
I have physics exam soon, this vedio really helped me , Thanks
Very mastered explanation ,thanks ,keep going for more videos
very clear explanation, thank you.
Congratulations for 100k subscribers
Hi Parth...
Please do a video about the Casimir force.
Excellent explanation!
was checking out how superfluids behave and if you needed a visual to get a feel for what this "same energy, all atoms" business means you should too. really helps develop the intuition.
Watching from Bangladesh and Proud of Bose
He was an Indian.
Proud of Bose but not for nationalistic reasons
And Einstein was a GOD
@@arihantvyas6271 he was also a Bangladeshi. A Bengali . he was the teacher of Dhaka University .
Milo Murphy's Law is the best show. Star vs is a poopy show
@@tanvirfarhan5585 If someone is a Bengali, it doesn't make him/her a Bangladeshi.Bose was a teacher in Dhaka university, but that was before the formation of Pakistan and Bangladesh, at that time India was united, there was no Pakistan or Bangladesh. Bose wasn't even born in Bangladesh, so no way he could be a Bangladeshi.
Took a minute to get here but, worth the trip. Thanks Parth!
Parth congrats with 100000 subs, and video I guess is an application of Arvin Ash’s video of superconductivity 🙃
Very nice explanation.
Thanks Parth, you are great man.
Great video!
Amazing 👌
Bro I am in 8th and understood most of it. Keep it up.....ur an awesome teacher :)
I was eagerly waiting for this concept becaise i was strange to this when my brother in 9th grade ask me about it i was quiet well thanks for this brother
Thank you so much
8:27 blew my mind, so cool!
Great video
Awesome man.
You're a legend bro!!! Thank you
Thank you🌹🌹🌹.
excellent
8:52, actually, this degeneration in energy disappears when including spin. technically, the electrons occupy two *slightly* different energy level, because of orientation of the elctrons with respect to the magnetic field induced by the "spining" charge (fine structure splitting). this conserves our intuitions about fermions again, because each fermionic state is going to be different energetically. there is always one quantum number used to desribe the system that is different for all fermions, and this will always lead to an energy difference.
Very good
Excellent video. Very interesting, informative and worthwhile video.
In this video, Parth made reference to his music videos and stated they're linked below. The linked path to said videos is a bit tricky. Click on the Parth RUclips site, then scroll down to Parth's Shenanigans and click. You'll then find a plurality of short music videos. Parth generally is playing tabla and an 8-string guitar and an electrified string instrument from India (North India, as I recall from previous encounters with this instrument). His skill is quite good and the videos are worthwhile. I've known many tabla players and they tell me it takes many years to be proficient at tabla. Parth is beyond proficiency at tabla.
Just a silly doubt. ;p As photons are also bosons is it possible to cool down and trap a bunch of photons and making them a Bose-Einstein condensate?
It's hard and not as straight forward as for massive particles. Since there is no conservation rule for photons, they just get absorbed by whatever they are in contact which. But it has been done in a non-standard way. Google it.
Expriments were done where at near absolute zero and in a vacuum where light was slowed to just 38kph.
Awesome
Just tapped to search for the video and got the notification
Great
Thank you! you've helped alot in my graduate Stat Mech course...but these integrals (Fermi-Dirac & Bose-Einstein) are killing me
proud of bose love from Bangladesh 🇧🇩 🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩
Please do a video on internal symmetries and fundamental forces
Sir you explanation is really outstanding.... plz.... Make a video on why the frequency of light is constant while passing through any medium..... I cant find...any answer and i am tired of finding... I cant understand other videos on youtube.. Plz.... Help me.... Thanks... For reading the comment... 😣☺
Hello!I love your explanation. Could you please make a video on Young’s Modulus ?I will be ever so grateful!🤍
I have probably never subscribed for someone so quickly.
Thanks Parth, for Including name in Your Video: Satyendra Nath Bose.👏🏽
One of the big questions in cosmology today (as I understand, it because I'm neither a mathematician nor a scientist) is, "The universe is at a somewhat low level of entropy today. So, by the 2nd Law of Thermodynamics, the early universe should have extremely low entropy. How is that possible?" My understanding is that the entropy of a Bose-Einstein condensate is zero. Perhaps the universe began, not as an extremely hot, dense state, but as a cold Bose-Einstein state reminiscent of LeMaitre's cosmic egg. This can probably work and would explain the entropy conundrum, but it would require a re-examination of some or our basic assumptions including the nature of dimensions themselves.
Please make a video on Lagrange hamilton mechanics virtual work etc..
Quantum Mechanics would be the next revolutionary knowledge we need to further advance our civilization. The discovery and understanding of atom made a significant change to how we are living and for sure if we manage to fully understand the magics of quarks, we could solve a shit ton amount of problems.
Hi - Love your videos. Can you give an example of a what can make a BEC. The only Bosons that I am aware of are the force carrier particles. Surely you meant something different when you said macroscopic..
Helium -4
Man, it's 2:30 in the morning. Why am I watching this..?
But you have new subscriber.
I'm kinda new to quantum mechanics so I don't have great basis on mathematics behind it. I understood the concept of bra and ket and the fact that vectorial spaces are used instead of normal sets.
I have 2 related questions:
1) what kind of mathematical relationship is |0>|0>? I know about inner product between bra and ket but it would be .
2) why the wave function is given by the relationship of question 1? (Talking about the very first example, at 5:42).
If more mathematical concepts are needed to understand this, could you please give me some resources?
Thank you so much for the content and for the help!
Kindly make a video on fermions and state how fermions are identical if fermions have opposite spin??
Currently trying to get my head around recent revelations that Fermions seem to be able to form room temperature BEC's...aka Coherent Matter, with rather weird properties with far reaching implications. If two electrons with opposite spin can occupy the same level, could this mean that they are capable of pairing up in potentially infinite numbers to form these macro-scale room temp condensates?
Hey parth what can i do for my future in area of physics beacuase im not good at cramming..
Hey im not path and if i am beeing honest im not even a physicist...
However i am defenetly a 14 year old physics nerd and im currently teaching myself University maths and physics. You say that you are not good at chraming. If you mean memorizing then dont worry, no matter how hard you will try you wont get far in physics if you just memorize stuff.
If you mean just having the paicients to sit and look at equations for many hours straight and still trying to understand them then i know what you mean...
Sadly, there is no solution to this. Its goddam hard but you will need to learn it. And here is s important tip: Also be paicient with the exercises!!! My biggest problem is that i emydeatly give up when i cant solve a problem in a book and just look for the answers. However, Problems in higher mathmatics and physics are built this way.
Shool is like: You learn how to add two numbers therfore your homework is adding numbers.
University is like: You learnd how to differentiate therefore we dont give you problems were you just differentiate because you already now that but instead we let you, for ecsample, proof a theorem by using differntiation.
Thats why such problems sometimes take hours. You are not used to finding the answer to a problem after an hour. In Shool you ether find it imediatly or not/at all(at least most times). So if you are new to higher physics and mathematics dont get this bad habbit.
I hope this helped.
Ps. Sorry for the bad english. Its my second language.
@@erikawimmer7908 Im 17 and i have also filled my brain with the basic stuffs of the universe and i want to dig deeper but cramming syllabus is the thing in which I'm no good.
@@adtex02 Yeah as I saied there is no way arrond sorry... You just need to cram those physics books. But it will get easyer whith time trust me!
Also: Two things are important.
1. Learn the math! I dont know if you also like math like me but it doesnt really matter. You need to learn much higher maths before you can really learn physics.
2. You say that you filled your brain with the basic stuff. Thats actually not as good as it might seem. If you learn university physics you will see that you will revisit everything important that you learnd in shool just in a mathematicaly much more rigourus way. So dont spend your time rewising shools stuff! Instead get started on the math emiedeatly get started on the math!
And use textbooks. Yes You Tube is a good sorce and there are many good resorces on the Internet if you dont have the money to buy a fifty bucks textbook for every topic but if you can then do it. And do as much and as hard exercises as you can!
@@erikawimmer7908 Tnx for having this conversation . I see the world has a bright future 😄
@@adtex02 I am happy that i coud help!😀😀
What does ζ(3/2) stand for in the critical temperature formula?
Can anybody please tell me
That's the Riemann zeta function. Zeta of 3/2 is the infinite sum 1/1^(3/2) + 1/2^(3/2) + 1/3^(3/2) + ..., which is about 2.612.
3:30 If I'm not mistaken bosons bunch up and fermions push away pairs.
Off topic but if at the edge of an event horizon the gravitational field strength is c^2 does that mean the relativistic circumference of a black hole is infinite?
I have one question sir , when we talk about hydrogen spectrum we usually talk about balmer lines. That is electrons jumps from higher energy level to 2 nd energy level giving out H alpha to delta lines. Hydrogen have 1 electron . Most probably it should be in ground state. So why we get hydrogen spectrum from higher energy levels to 2 nd energy level??
Light is a kind of a transverse wave with a frequency, when it hits matter , matter gets disturbed at the same frequency, matter will disturb neighborhood matter in the same frequency,
Matter should emit its own energy at a lower energy. Or frequency
Hello, Thanks for your video, somebody asked me: "can bose-einstein condensate as 5th state of matter change into fermionic state? Like in melting ice that solid changes into liquid " , I'd really appreciate if you could answer it.
So far Quantum physics is the most confusing subject for me since I have been introduced to it....I can remembere all the fact about it....but whenever I think why does scientists assume perticular particle(electron).... In state of superposition.... whenever i search about it everyone explains shrodingers cat expriment ...but I cant relate it to electron....Would you please explain it?
Thanks for the video, I do have a question though: atoms are made of fermions (electrons, protons, neutrons), so how do you create a Bose-Einstein condensate (which I believe is made of bosons, not fermions) by cooling atoms?
There's a book by Amanda Aftalion called Vortices in BEC. There's a section dealing with experimentally making a condensate or you could look some papers up in libgen or Google scholar. This would be better in explaining how to experimentally make an exotic state such as this I think.
Some atoms are "composite bosons" because they have an integer spin when you add up the spin of all the particles. For example, helium is made up of 2 protons, 2 neutrons and 2 electrons. The sum of the spins of all those particles is 19 (1 for the 2 electrons and 18 for all the neucleons). Making Helium act like a boson in some circumstances.
What kind of equipment is required to make these observations?
I keep getting lost in thought while I listen to this.
Would it be possible for fermions condensate behind an event horizon
Which bosons are normally used for this?
the video was superb, but i have a question. in the formula of critical temperature, you mentioned mass of bosons.But bosons are massless , as photons are one of them. how can we account their mass?
I assume by using their relativistic mass from E=mc² (their Energy can be seen as a virtual mass). In general, the definition of "temperature" for photons is tricky, so we define it as the average energy of each photon (similar to the average kinematic energy of each molecule)
Doesn't ideal gas particles, or simply the molecules constituting it, behave like bosons? Because there is no restriction to them being confined to one or the either energy states. So what's the difference?
Ideal gas is just the simplest model describing behaviour of gases with the assumptions that the particles don't occupy any space, they do not interact and do not change phase. There actually are no "ideal" gases, but the closest thing we have to 1 is helium.
This really can't be compared to something like bose-einstein condensate.
Does this mean that the pauli exclusion principle doesn’t apply to bosons
Are two photons with different wave number identical i.e bosons
Of distinguishable?
But I still have a doubt. Is it flowing like fluids or does it stay in it's place like solids? If it is neither solid nor fluid then doesn't that mean it'll neither flow nor stay in it's place ?
I was led to beleave that matter can form bose-einstein condensate. But matter is formed from other things not (only) bosones. Im confused, can someone clarify?
How to convert fermion to bosone? Did gravity can change this rules and force fermions to be in one energy level that mean transform it to bosen or pseudo-bosone or bosone-fermion and uniform it with other bosone convert it to some new partiical that can exist only in black hole because only there is so much gravity force larger than every forces even stronge force.
I have learn bose Einstein distribution and i have a confusion
Firstly i read that partials in same cells have equal energies then i read about subcells in a cell so tell me plzzz does particals have different energies if they are in same cell but different subcells
And this confusion firstly came when i study bore model according to bore energies are same for same cell but then my teacher said lower energy subcell must be filled first but how can a subcells of same cells have diff. Energies
what happens if we try to bring the fermions to the lowest energy level by cooling it?
I understood nothing, but it was a good video.
Wave function as in scalar?
… yes. I agree.
Out of topic, what happens on a multiple potential well system? What can change, energy, wave function, energy spacing etc and why is this?
Is it possible that there's a new particle we don't know about at play here, rather than a new force?
how we know that mass and charge of an electron is always constant to another electron?
It's just a law of the universe. Every single electron is completely identical
If it wasn't, things would be very weird indeed.
Why do Fermions have half spin?
Satyendra Nath Bose is like a super hero name lol.
I can't be the only one who saw the movie spectral and wanted to learn more
Wait a minute. I thought the whole idea of the BEC was that genuine took on a bosonic state and acted a a single entity (of course I'm just regurgitating what I thought I understood from a few other RUclips videos).
I am puzzled of how bosons preserve quantum information. I get that fermions do that given that this class of particles are not allowed to have the same quantum numbers, hence occupy the same state at the same time, am I getting this right?
Bosons and fermions should both preserve quantum information, isn't it?
Path if kind enough, maybe to explain how that is happening in the context of QM, or let me know in a short message (it's been troubling me for some time, I'm just lacking the understanding in connecting these).
Kudos for all your material, big fan from your first video I’ve seen ;)
Sir i have a confusion that if identical particles means tha every property like mass ,charge، spin etc are same ...than how we can say that fermions are identical as fermions have two opposite spins +1/2, -1/2....if fermions have opposite spin then why we call fermions are identical and indistinguishable?????? it's confusing me a lot....😩😩
I'm gonna name my business as BOSS EINSTEIN CONDENSATE Inc
Hi.
maybe this at-absolute-0-matter-behaviour is a noticeable to macroscopic scale proof of wave matter?
- When all matter is at absolute 0 , then there is no entropy at all, and only synchronized quantum field excitation left, all particles, or rather matter waves , are now synchronised, creating one big macro-scaled quantum system, that`s my understanding of B-E C effect.....
I'm having a mental breakdown rn and I chose this out of curiosity
I am also having a difficult time and turn to youtube for distraction. personally, I like it because this sort of thing is interesting, but beyond that a little inspiring, that something more beautiful exists in the universe. best wishes for you.
When we solve |phi_{A,B}|=|phi_{B,A}|, we get any phase shift like phi_{A,B}=e^{i x} phi_{B,A}. When we look at x=0 or x=pi I guess this defines bosons and fermions but what about the rest ?