The Basic Math that Explains Why Atoms are Arranged Like They Are: Pauli Exclusion Principle

[@ParthGChannel]

Hi everyone, thank you so much for watching and supporting this channel! Please check out my quantum mechanics playlist for more videos like this one: kzbin.info/aero/PLOlz9q28K2e4Yn2ZqbYI__dYqw5nQ9DST

[@kimberlymarkus6387]

Einstein taught us that one experiences time to go slower when one approaches the speed of light. In theory, a photon should not be able to experience time. So are they in one dimension less than us or would they experience another dimension? Sorry if this is stupid 😅

[@nickangelos7221]

@@kimberlymarkus6387 great question! physicists tend to think of time as the fourth dimension but that is purely conceptual. Photons (which are bosons) travel at c in empty space independent of time. If we had four spatial dimension (x,y,z,w) then photons would travel through all four of them.

[@kimberlymarkus6387]

@@nickangelos7221 thank you ☺️

[@SALESENGLISH2020]

Finally all these things are making physical sense. Thanks Parth! I wish millions of high school and college students would watch these videos, think, understand and not be scared of physics. The problem with most textbooks and teachers is that they state "It is so" but do not explain why and why not, what could be an exception and its implication and so on. That's why I always liked people like Wolfgang Pauli. It is said that if he entered a lab, all the experiments would go wrong.

[@arvindiyer1649]

Haha, 1 high school student here

[@SALESENGLISH2020]

​@@arvindiyer1649 Good. Even most college students need help. So, I will edit that part now. Thanks. Best wishes.

[@lilac2698]

@@SALESENGLISH2020 I'm another high school student who began high school only a few months back, we've only just begun learning about atoms' structure and molecules, but I ended up learning every single thing all the way till the Pauli's Exclusion principle because I looked at the atomic number of Xenon, and the 2n² rule we were taught (Maximum no. of electrons in a shell where n is the energy level) didn't seem to hold true, and it confused me a lot. This ended up making me find chemistry and quantum mechanics highly interesting, and I binged everything I could understand without insane mathematics and symbols.

[@SALESENGLISH2020]

@@lilac2698 Superb! All the best.

[@asgovindarajan5597]

Parth sir, I really wish teachers like you are invited as the Chief Guests! You deserve all the praise in the world for simplifying physics concepts in an intuitive and joyful way, for literally everyone to learn! Please keep going sir! I'm indebted to you a lot, for learning a ton from you!

[@satyamverma101]

bro lol thoda zyada ho gaya. bahut makhan laga liya

[@asgovindarajan5597]

@@satyamverma101 😂😂 theek hai bhaii! But mujhe itne saalo baad pehli baar ek achi physics teacher mil gya hai us khushi mein bool dhiya. 😂😉

[@squidly1369]

@@satyamverma101 makhan kya bro isme ye ek sikhne wale ke dil ki awaaaj hai lol xd ...

[@integreat2890]

Hey Parth, could you make a video on Liouville's theorem?

[@ranjitsarkar3126]

That is a maths theorem and this is a physics channel

[@integreat2890]

@@ranjitsarkar3126 Liouville's theorem is also used in Classical Mechanics and it's important for theoretical physicists.

[@amreshyadav2758]

this man have a crystal clear concepts. you beauty, parth legend.

[@bradchun21]

Wow. Clearest explanation I have seen yet on PEP. Thank you!👏👏👏

[@henryD9363]

KZbin just recommended your excellent channel and I'm very grateful. I've only watched a few videos and intend to continue on. But I have a bit of a quarrel! I will make an assertion regarding electron/fermion spin direction that is very incorrect: There is a direction in the universe such that the spin of any electron is parallel or anti-parallel to this universal (up/down) direction. This direction is a fundamental property of the universe. There's nothing that you have taught us that contradicts this assertion. I believe a lot of your viewers may be learning about spin direction for the first time. Your statement that an electron spin is up, down or both, implies that there are no other directions available. So I would suggest that, since this direction is arbitrary in the sense that it's CHOSEN freely, you should briefly mention this very important fact at the outset. Apologies if you have already covered this topic before. But it's worth a half a sentence to be repeated! Thanks

[@rakshitverma5016]

Amazing video. The thought at the end about electrons being fermionic kind of indistinguishable is responsible for life and the universe we see around us is kind of mind-blowing.

[@mwafrikahalisi2549]

Yes, because that's the principle behind the existence of all the elements in the periodic table.

[@Threshold.edu1]

I love your videos. The way you present physical structures are mind-blowing

[@Tyletoful]

Just discovered your channel. I've liked and subscribed. This is a great explanation.

[@gummy425]

Wow wow wow! I enjoyed this video from start to finish. Definitely earned yourself a subscriber

[@Pexl_]

lovely video parth keep making more vids like this

[@job2687]

I had so much trouble with this but you explained it so clearly, thank you!

[@moonpearl4711]

at 2:46 why is it, that ψ(A,B) = +ψ(B,A) or - ψ(B,A)? And why are we not also considering -ψ(A,B)?

[@bradleywalsh4103]

Loved the video my friend. Simple and to the point. Cheers

[@Eztoez]

What a thoroughly beautifully explained video. Thank you. I've only ever seen one video before that clearly explains the Pauli Exclusion Principle, but yours is better. You've got the right amount of mathematics in it. Not everyone has Masters degrees in mathematics, as some videos assume, although I'd like to know more about Hamiltonians, Lagrangians, and Fourier Transforms. I don't know if you've done videos on those.

[@bhaskarmangaraj7527]

Your teaching is great ! I wish if you can make some videos dedicated to mathematics like a playlist of tensors or other mathematical topics needed in physics

[@levinunemaker4365]

9:38 "Assuming our understanding of QM is at least relatively correct"

[@priyanshi6507]

Awesome job bhaiya😬

[@alfredosolari7597]

Yes, I did enjoy the video, also,because you explained such a complex topic as clearly as anyone could. I am not a scientist.However I do like science.Naturally I have subcribed to to your channel and given you a 'like'. Many thanks sir.

[@heinzriemann3213]

This channel is going places.

[@mansoorsiddiqui7396]

As always brilliantly simple!!

[@divyanshugreninja6692]

Sir , please make videos regarding the vacuum energy and all those related stuffs . I have grown interest in physics on seeing your videos . Keep going sir

[@pedrogrimaldisemeghinimart759]

That’s an amazing explanation dude, just fantastic!!

[@padraiggluck2980]

Makes one’s head spin thinking about just how atom formation took place in the early universe.

[@neelakandan.v.m2991]

Excellent explanation.

[@das250250]

A very well presnted video ,as usual. Care taken in the right spots. Beautiful how you attach the mathematical model to explain why the exclision principle exists. What is an interesting thought is that you say if the electron occupies the same spot with another it superimposes into a boson. The thought i have then is , is a boson a superposition (reflection) of fermions superpoitioned

[@minecraftrtx2894]

Thanks parth for wonderful content

[@eriktempelman2097]

Many, many thanks for this!

[@eggyfebrianto4533]

Super duper helpful, thanks a lot 👍

[@A.B.A277]

I just can say god blesss you, I finally got it with a source

[@huwphillips2696]

Absolutely brilliant video

[@stefaniag4167]

Excellent job!!!!I found recently your channel...I have to admit that i am excited by your effort!!! could you make a video about Dirac's equation ?????

[@zainkhalid5740]

just needed this topic!

[@drshafqat9291]

Simply superb n fantastic

[@muklpsarma]

Proud of you parth...I love to become your student....

[@bragoen]

Hi Parth, as always your videos are very good at giving a grasp to complex prolem. Would you someday make a video on Feynman's diagram and explain for the layman what's so special about them, did they allow for something new or are just a cool doodle trick ? While I can read the wiki page what make them unique or such a contribution has always escaped me.

[@deepyaa3392]

Hey Parth ,can you make a video on your favourite Physics books/STEM books in general which don't involve math beyond high school level?

[@jacobhaddo1180]

I'm not Parth (obviously), but I just started Leonard Susskind's Theoretical Minimum lectures which are very informative and seem to fit what you want

[@informationparadox387]

Well that was kind of BaSiC concept which is not really hard to find...So please can you start these concepts with some mathematics , it would be quite helpful!😌 B/w your videos are always great!

[@Pexl_]

i have a quick question for you parth how can the fucntion be positve or negative during particle exchange? does it have to do with some maths? or Just the way they work?

[@animalbird9436]

Its all maths..they cant see it so if the math fits .thats how its done...hence the is maths reality crap..reality is math and math is probably reality lol 🤣🤣

[@xolisanincubencube4725]

Thank sir you nailed it🎉

[@kevinmccarthy8746]

Thank you Parth. Love the shows.

[@question_mark]

an actualy successful attempt of representation of my feeling : 👌👂👁👄👁👂👌👌 👌💧👌 💧👌 👌 💧👌

[@meymeyM7]

I feel u lmao

[@rukmaninivetha8421]

Wow.... It was awesome 😍

[@Katia_777]

Thanks. That was really useful

[@amirtambe2957]

No frills. Crisp. Liked.

[@roshanzehra9827]

Hi, Parth just saw your video and its amazing , i am 17 years old and very attracted to physics , i am going to be a physicist , if u have any tips for mr please tell me , i take u as my professor . Thanks alot

[@theartofmusic05]

Good explanation Parth 😊

[@gokuls7061]

HI PARTH, YOUR TEACHING IS AWESOME, APART FROM MY PROFESSORS, I'M LEARNING FROM YOU. KINDLY MAKE VIDEOS ON LINEAR VECTOR SPACE.

[@utkarshpuri3739]

favorite channel

[@ethanfreeman9243]

Great video as always. Is it possible to make a video on Bell Inequalities please?

[@adamgrimsley2900]

This is good, subscribed

[@dantefernandez2455]

Wonderful video as always! Just a lingering question, Parth. It seems the Pauli-Exclusion principle is just a bit of math that models fermionic behavior quite well, but it doesn't answer how fermions 'know' the state of the other. Why and how do they do that? I feel I am misunderstanding some basic things here because it would appear every particle is just really good at math, lol.

[@ARVash]

In my other comment I took a stab at it, I think it's because they take up space. in QM though I think it's because they share a wave function and there's constructive/destructive interference at two points. Kinda like the sand on this sound plate, turn your volume down... kzbin.info/www/bejne/j5bHmKiYh7-pl5o

[@artberman5825]

What are the L and M distinguishing factors?

[@VSHEGDE1947]

L is the azimuthal quantum number which gives the subshell to which the electron belongs, and M is the magnetic quantum number which gives the orbital to which the electron belongs

[@JackJackKcajify]

Ah but parth you are misunderstanding what math is and isnt. There is a uniqueness to the structure of the underlying fields. This structure is explained via mathematical models. But FUNDAMENTALLY, it is a PHENOMENAL UNIQUENESS of the field. It is a mathematical description and model of the phenomenal data. Its not that the energy levels are determined based on the mathematical structure, its the other way around. Its a mathematical treatment of phenomenal data.

[@mastershooter64]

Hye Parth can you please explain Feynman's path integral formulation?

[@sumansaha552]

Thank you❤🙏..

[@putinscat1208]

All this makes perfect sense. However, is Pauli exclusion just something that was observed and a model was created, or can it be proven mathematically?

[@SWRDMaster]

How about a video related to electrons coexisting in Cooper pairs?

[@ankitthakurankit4764]

3:03 how we know the first eqn. Is for bosons and second is for fermions??

[@mnada72]

9:30 May be the life we know about wouldn't exist but sure another sort of like would exist. Let's rephrase it if any single item in the a system changes all other items need to change also for a system to exist may be in a different form

[@aodoemela]

Can you please do a video on the pilot-wave interpretation of quantum mechanics and how it differs from the Copenhagen interpretation then share your views on which you think is the correct interpretation. :)

[@iansagar1785]

Hey Sir I have a question !! Do light Can bend space-time ?? (as it is produces electromagnetic field, Moreover it has energy and momentum ! And Can cause stress ! ) So Can light Bend space-time too ?? I didn't get the precised Answer anywhere !! Plz help ! @Parth G

[@drsonaligupta75]

Isn't wave function a complex number so if their modulus is same so why cant one be i times (√-1) the other one or something. Why necessary negative or positive?

[@HarryPotter-ov3kv]

I'm confused: electrons are indistinguishable but aren't allowed to have the same quantum state? Pls help me understand

[@דודרנדלמן]

Hey parth, could you make a video on the quantum mechanics of a knuckleball? ⚾️

[@kimtaiferragamo]

THAT WAS AWESOME

[@Rose-ff3fi]

Thank you

[@adamjondo]

Great Video. But what are L and M @7:50?

[@bhaskarmangaraj7527]

can you please make a video on lorentz transformation

[@ppmendonca1]

Why does the n=1 only allow fermions of differing m_s but not of the other quantum numbers, while the other n=* allow other quantum numbers to be different?

[@courage936]

so basically electrons are indistinguishable from each other, yet have opposite spins, got it : (

[@robertknetsch2715]

This makes a lot of sense. But what I have never seen is why is is that fermions obey this "law" of Pauli's Exclusion Principle, yet Bosons (e.g., photons) can simply "ignore" this law, say, in a laser where all photons are at the same state. What is the property of fermions that make them "have to" follow Pauli?

[@randommcranderson5155]

the property that cause the Pauli exclusion principle is that fermions have anti symmetric wavefunctions. More information and visualization here: kzbin.info/www/bejne/kJ3TY3qHaLR_m6c

[@ethanfreeman9243]

okay but how come the other quantum qualities dont apply to the n=1 shell. i.e. more than two because you can have differences in the other values, like in the other shells?

[@WilliamDye-willdye]

What is the property that allows electrons to be in the (otherwise) same state as long as they are in different atoms? I've read that it's the "position" which differs, but wouldn't electrons on opposite sides of a large shell also have different positions? Maybe I just need to read the explanations more carefully, but so far it isn't yet clear to me.

[@scollyer.tuition]

An electron in an atom is in a so-called "bound state"; it has a definite energy and it is more likely to be near the nucleus than far away - the wavefunction tends to 0 as we go far from the nucleus. For two identical atoms, say two H atoms, we can compute the "overlap integral" for the wave functions of the two electrons; the overlap integral essentially measures the probability of the two electrons to be close together. Given that the wavefunctions tend to 0 far from the nucleus, the overlap integral will be small when the atoms are far apart. When the overlap integral is small, the probability that the electrons will occupy the same state (i.e. will have the same 4 quantum numbers) is large, and the exclusion principle is essentially "switched off"; when the overlap integral is large (when the H atoms are close), the probability that the electrons occupy the same state is small i.e the exclusion principle is strongly "switched on". When the atoms are very close, the overlap integral is close to 1, and it's exceedingly unlikely that the electrons have the same 4 quantum numbers. When the atoms are close, new energy levels become available in the H atom, (and so new energy quantum numbers), which ensures that the electrons can have different quantum numbers in the two atoms. So, for example, the 1s orbital splits into two new orbitals, one with slightly higher energy than the original, one with slightly lower energy. If we bring close together two H atoms whose electrons have opposite spins, they can both occupy the new lower energy "1s" orbital, and a low energy H_2 molecule forms, parahydrogen. If we bring close together two H atoms whose electrons have the same spins, one occupies the new higher energy orbital, the other occupies the lower energy, and a higher energy H_2 molecule forms, orthohydrogen. So the formation of new energy orbitals is important in the question of molecular bond formation (and in understanding the properties of metals and semiconductors, and so on). Caveat: this explanation is very simplified, and for more info, you may want to look at the subject of Molecular Orbital (MO) theory, beloved of chemists, and with which I only have a passing acquaintance.

[@WilliamDye-willdye]

@@scollyer.tuition Thank you!

[@donegal79]

fantastic

[@abhayiyer8864]

Can we force 2 similar electrons into the same energy level. What will happen in that case?

[@sagarrawal8332]

May i know how you make your animation using which softwares. I reaaly liked the demonstration and willing to learn for my presentaion in my physics class for my students

[@akashsudhanshu5420]

I am trying to think of something that is unique.(to explain indistinguibility) - it's like waves are spread upto entire universe. And we can't confirm two waves are exactly similar.

[@ankitthakurankit4764]

Bhaiya the exceptional electronic configuration of chromium is explained by the stability in half or fully filled orbitals due to law of symmetry and exchange energy can you explain both in detail 'coz law of symmetry seemed useless to me the textbook says we know that symmetry leads to stability i think this is pure junk i mean why should symmetry lead to symmetry???

[@simonhanson5990]

Am enjoying these videos very much, thank you Parth. Can someone help me understand though that if electrons may have spin up or spin down, or have other different quantum numbers or exist on different energy levels; how is it that we can then say electrons are indistinguishable? I am probably missing some point here but if anyone can clarify this for me that will be appreciated. Cheers

[@mohammadhusein5061]

could you explain the neutron or electron degeneracy in M dwarf star

[@MisterTutor2010]

Symmetric vs antisymmetric entirely depends on whether spin is integer or half integer.

[@bjarnivalur6330]

Hey, Parth, I've been wondering, your accent sounds very British but you use V for potential instead of U which I always thought was an American custom. Where are you from?

[@divyanshugreninja6692]

Hey sir , I have a question. Why is it that the fermions can't occupy the same quantum states as directed by the Pauli exclusion principle ? Is there some reason behind it ? And when do we represent the superposition of the fermions it's negative in between the two states and while in bosons it is plus between the two states ? Why is it so ?

[@randommcranderson5155]

it has to do with the properties of waves - when waves are both the same sign they reinforce each other, and when they're opposite signs they cancel out. a good video on this topic here: kzbin.info/www/bejne/kJ3TY3qHaLR_m6c

[@davidsweeney111]

are the shapes of atomic orbitals mathematically optimised based on some law, eg least charge repulsion?

[@SamraiCast]

How can I distinguish between different bosons?

[@ethanfreeman9243]

Hey, could you provide a simple explanation of Maxwell’s equations please! nice video

[@ParthGChannel]

I've already made a video for 3 out of the 4 equations! Check them out here :) kzbin.info/aero/PLOlz9q28K2e6aNgl1zt1xccyy4Ofl3YAk

[@ethanfreeman9243]

@@ParthGChannel Just checked them out amazing videos. Thank you so much for making this type of information easy to comprehend for the average person😊

[@mahmoudmroweh7730]

​@@ParthGChannelhey parth when we say that 2 electrons could found in same energy level is that implies they can be at the same position at the same time or they are in diffrenent places in the energy shell and my second question is could bosons that have mass occupy the same position and if that possible shouldn't we get a poinr containing 2 bosons of heigh energy and heigh condinsation I hope you answer me thank you

[@erikawimmer7908]

Whut up my physics boys we are back at it again. Hows everything going for you?

[@erikawimmer7908]

@@user-pz1gd3nv4n well look at i that way: if it were so then you woudnt exist lol

[@nilanjankmukherjee234]

Namaskar dada.. G for Ghosh naki?

[@charmingissam6002]

hey . can you talking about Superconducting Materials

[@sauravyadav4445]

What a explanation

[@bobkat8765]

If I understand this correctly, it’s not “banning”, it’s destructive resonance. If the exclusion is “caused” by destructive resonance, there must be a pair interacting, and at any given instant, one has an attribute value and the other has the opposite value. So isn’t that HIDDEN rather than excluded?

[@Gleem]

Parth special request from a listener before you hit 10,000k I would really like to know more/for you to cover one of the biggest scary taboo topics in Particle Physics: Aether. On my investigations aether is a concept which most of science is based on, Newtons Gravity/Lorentz-Einstein's Space-time "New Aether"/Maxwells Equations/Paul Dirac's Negative Sea or Hole Theory, all have required the notion that there must be something in the background instead of an absolute void. More recently in the 21st centaury you have the likes of John Bell preferring to use Neo-Lorentzian Relativity over Einsteinian, Leon Lederman and Robert Laughlin publishing books explaining that the Quantum Background is a relativistic aether brought back from Einstein's incorrect removal, where even in letters to Lorentz and his 1938 book both explain he was wrong to remove the concept of aether, he only should have removed the measurable velocity of it, and stated that General Relativity is identical to Neo-Lorentzian Aether and therefore Aether lives on as a concept. There seems to be a lot of miscommunication from science communicators and generic sources on the internet who literally point blank state "Aether was debunked in 1887 with the Michelson-Morley experiment" but reading the original paper and the reactionary fact that Lorentz designed Length Contraction and Time Dilation to avoid removing it completely just because it was undetectable, this seems like a fabrication and MMX only removed a detectable absolute framed aether, not Lorentz' Relativistic Aether. What are your thoughts/knowledge on the topic? Here are some of the cites I mentioned, although every time I ask people of even PhD level, they stutter and I get accused of cherrypicking, so there definitely is ambiguity and lack of knowledge. Yours "lacking-input-and-need-yours", Gleem haha ----------------------------------------------------------------------------- “The aether: Invented by Isaac Newton, reinvented by James Clerk Maxwell. This is the stuff that fills up the empty space of the universe. Discredited and discarded by Einstein, the aether is now making a Nixonian comeback. It’s really the vacuum, but burdened by theoretical, ghostly particles.” Leon Lederman - God Particle: If the Universe Is the Answer, What Is the Question? - 2006 books.google.co.uk/books?id=-v84Bp-LNNIC&pg=PP15&dq=leon+lederman+%22ghostly+particles%22&hl=en&sa=X&ved=2ahUKEwivuN-kvcHsAhVMShUIHZbDDgQQuwUwAnoECAQQCA#v=onepage&q&f=false ----------------------------------------------------------------------------- "....Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo” Robert B. Laughlin - A Different Universe: Reinventing Physics from the Bottom Down - 2005 archive.org/details/differentunivers00laug/page/120/mode/2up ----------------------------------------------------------------------------- “We can now see that we may very well have an aether, subject to quantum mechanics and conformable to relativity, provided we are willing to consider a perfect vacuum as an idealized state, not attainable in practice. From the experimental point of view there does not seem to be any objection to this. We must make some profound alterations to the theoretical idea of the vacuum. . . . Thus, with the new theory of electrodynamics we are rather forced to have an aether” Paul Dirac “Is there an aether?” 1951 Nature vol. 168, pp. 906-907. www.nature.com/articles/168906a0 ----------------------------------------------------------------------------- “The approach of Einstein differs from that of Lorentz in two major ways. There is a difference of philosophy, and a difference of style. The difference of philosophy is this. Since it is experimentally impossible to say which of two uniformly moving systems is really at rest, Einstein declares the notions 'really resting' and 'really moving' as meaningless. For him only the relative motion of two or more uniformly moving objects is real. Lorentz, on the other hand, preferred the view that there is indeed a state of real rest, defined by the `aether', even though the laws of physics conspire to prevent us identifying it experimentally. The facts of physics do not oblige us to accept one philosophy rather than the other.” John S. Bell - Speakable and unspeakable in Quantum Mechanics - 1988. www.google.co.uk/books/edition/Speakable_and_Unspeakable_in_Quantum_Mec/FGnnHxh2YtQC ----------------------------------------------------------------------------- "I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter." Hendrik Lorentz- The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat - 1916 www.jstor.org/stable/41133827 ----------------------------------------------------------------------------- Einstein also wrote in a 1919 letter to Lorentz: “It would have been more correct if I had limited myself, in my earlier publications, to emphasizing only the non-existence of an ether velocity, instead of arguing the total non-existence of the ether, for I can see that with the word ether we say nothing else than that space has to be viewed as a carrier of physical qualities.” Einstein stated in his 1938 book, The Evolution of Physics: “This word ether has changed its meaning many times in the development of science. … Its story, by no means finished, is continued by the relativity theory.” www.independent.com/2012/07/20/higgs-field-new-ether/

[@صوفيا́-ب1م]

Yes

[@eriktempelman2097]

As follow-up, can you expand on the higher shells?

[@ARVash]

I mean isn't this a long (and more specific) way of saying that electrons take up space, which doesn't strictly need a QM description because there are EM fields?

[@mairisberzins8677]

Parth, why do you always keep saying to find the probability of finding a particle at some given location, we square the wavefunction, (technically square the modulus). Why do you always accent the modulus part, and what difference is there between a plain squaring of the wavefunction?

[@shreyassingh7721]

I think its because the wavefunction is actually a complex number, so squaring it would get you another complex number. You have to take its modulus (a real number) and square that (alternatively multiply it by its conjugate which does the same thing).

[@DrDeuteron]

the wave function at x is a complex number a+bi, and: (a + bi)^2 = a^2 + 2abi -b^2, so the plane square is complex...not good for a probability. The modulus is positive definite: |a+bi|^2 = (a+bi)(a+bi)* = (a+bi)(a-bi) =a^2 + b^2.

[@mairisberzins8677]

@@DrDeuteron Ah yes. I completely forgot about squaring a complex number. Thanks

[@firozr4842]

Parth , do you have an e-mail I can reach out to . Also what software do you use for the graphical representation in the video . Thanks Firoz

[@TheHumanHades]

What are those red circles of light on your glasses. I have seen them in almost all the videos now.😂

[@jagadishc3143]

How do we know that hydrogen have 1 electron and how do we know n shell has only 2 electron Can u please explain these kind of basic questions

[@gauravkumar4450]

We found a proton paired with an electron and named that atom Hydrogen. Nothing special about it. You can look its history up. Each n shell has orbitals that are named as "s, p, d, f, g, h, ..." (they are determined by quantum number L that Parth has not discussed) and each orbital can hold a certain number of electrons (that in turn is determined by quantum number m_L that too Parth has not discussed). So, for n = 1 shell, it has got only s orbital and no p, d, f etc. Now, s orbital can hold only two electrons (one spin up and the other down). I am not Parth, but I hope that answered your question.