Bose-Einstein Condensate: The Quantum BASICS - Bosons and their Wave Functions (Physics by Parth G)

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.

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[nigelmaccuver]

SN Bose was probably major figure in science who is very much underrated and goes unappreciated.

[ArvinAsh]

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.

[roninapparition]

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!

[subhomoygupta]

The best illustrated explanation that I needed for quite some time now.

[catxnc]

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.”

[l_zonnacraft]

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

[natealbatros]

Wow 100k, congratulations
To 1M and beyond

[adamcummings]

I'm gonna be doing my master's dissertation on BECs so I definitely will be binging your videos along with others. Thanks :)

[praveenb]

Hi Parth...
Please do a video about the Casimir force.

[janhorak]

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.

[sharatshastri]

I have physics exam soon, this vedio really helped me, Thanks

[vincenthubschmann]

Funnily enough this helped me greatly in getting a better intuition for the Pauli exclusion principle. Thanks a lot!!

[IsmailKhan-]

Bro I am in 8th and understood most of it. Keep it an awesome teacher :)

[halilibrahimcetin]

I am amazed by the explanation.
This video leads to open new horizon in my understanding on Bose-Einstein Condensation.
Thanks for the sharing.

[k.mshariatullah]

Watching from Bangladesh and Proud of Bose

[alexkaapa]

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.

[Viureify]

Just recently discovered your channel and I must say it is amazing. Thank you for providing such great quality content!

[robertschlesinger]

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 YouTube 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.

[englishinenglish]

Parth congrats with subs, and video I guess is an application of Arvin Ash’s video of superconductivity 🙃

[ankit]

Sir you explanation is really outstanding.... plz.... Make a video on why the frequency of light is constant while passing through any 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... 😣☺