I'm not trying to be pedantic here but why do we accept indirect proofs in a system which allows superposition of a matter of fact about the physical world and its logical negation? Asking for a friend.
How can i calculate that psi function? It has r1, r2 two variables. I can feel by integrating spherically with Energy operator and be able to get only one energy value. But i can't imagine what psi square(possibility) would be
Hi semispecula, my question s are 1) @3.52 you said the spatial becomes antisymetric after filiping ab to ba, my question is why is this so??? 2) if instead two electron if we take one positron and one electron then also total wave function become zero when they are in same position. So why positron electron wave function is allowed and while electron electron wave function is not???
Hello Pritam, let me try to answer two of your questions. 1) When you flip the labels of two particles, such as changing "ab" to "ba", the wave function of the system changes in a predictable way. In the case of fermions, electrons for example, the wave function must change sign when we swap two particles. This is because of the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously as I mention in the video. To see why swapping two fermions requires a sign change in the wave function, think it this way; consider a two-particle system with wave function ψ(ab), where "a" and "b" represent the positions of the two particles. Swapping the labels of the particles changes the wave function to ψ(ba). The wave function must be antisymmetric with respect to particle exchange, which means that ψ(ab) = -ψ(ba) This makes sure that the probability density remains unchanged under particle exchange. 2) When two electrons are in the same position, the wave function must be antisymmetric due to the Pauli exclusion principle that I explained in the video. Since the total spin of two electrons is always either zero or one, the wave function must be antisymmetric in both cases. This means that the wave function must be zero when the two electrons are in the same position. However, an electron and a positron can have a symmetric wave function if their spins combine to form a total spin of zero. What I mean is that the wave function can be non-zero when the electron and positron are in the same position, as long as their spins are in the correct configuration. I hope it helps! Have a great day.
@@Semispecula Thank you sooo much! I kinda just said that taking the root of "ψ² (a, b) = ψ² (b, a)" to get the wave functions can give you a positive or negative value after exchange. The positive for bosons and the negative for fermions. I hope that will do cuz I already submitted the draft haha
Great question, well as the lecture video states, electrons can not have the same quantum numbers in the same place. However in the first orbital, we can have maximum 2 electrons with different quantum numbers. If we had three, two of them would be identical and as the lecture video states this can not be so. Hope it answered your question, if not feel free to ask for more elaboration.
@@Semispecula thanks for answering! My question was more about why it cannot have the same quantom numbers? Like, why is there such a rule? How did the scientists find it out?
@@Почемучка-т6в Well, once we have the same quantum numbers, as I talked about in the lecture video, the wave function turns to 0 and that makes having same quantum numbers not possible. The way scientists found out was with the formulation in the video. I hope it helps!
So basically no two electrons can be at same place or elese they are just 1 electeon.if all quantam numbers are same then they are same place whivh is not possible is what i get
Fermions satisfy the Pauli Exclusion Principle because fermion identical particle wave functions combine antisymmetrically. And they are antisymmetric because they satisfy the Pauli Exclusion Principle. (ie - a tautology). Bosons do not satisfy the Pauli Exclusion Principle and they have symmetric wave functions. And um... we don't know WHY -- that is just the way the universe works. It is an assumption (sort of like an axiom in mathematics) and no proof is needed because -- it works and is consistent with what we observe in nature. It is turtles all the way down.
They are waves and for some unknown reason, when you combine the waves of two of them, the part of the graphic where is more probably to find the particle, its always in different spots, never close to each other, and this fact creates a "false repulsion."
it's a classification. So fermions are antisymmetric by definition. Now, why there are any antisymmetric particles/fermions in the world at all (instead of, for example, them all being symmetric), I have no idea.
I'm not trying to be pedantic here but why do we accept indirect proofs in a system which allows superposition of a matter of fact about the physical world and its logical negation? Asking for a friend.
Great explanation ✨✨
At 1:48 spin can be "positive 1 and a half or negative one and a half", uh shouldn't it be positive half or negative half?
Damn puberty hit hard
it's not just antisymmetric though it's also noncommutative. Pascual Jordan was very happy when his noncommutativity was proven by 1/2 spin.
Good explanation
How can i calculate that psi function? It has r1, r2 two variables. I can feel by integrating spherically with Energy operator and be able to get only one energy value. But i can't imagine what psi square(possibility) would be
Can the quantum number n assume zero as value or only any integer > 0. What’s the meaning of n = 0?
Decent explanation
I think you could've spared a minute to explain why the conclusion that Psi=0 is absurd.
That is a lovely idea. I somewhat assumed it settled but making a separate video for the matter might be useful.
5:53 missing brackets
Hi semispecula, my question s are 1) @3.52 you said the spatial becomes antisymetric after filiping ab to ba, my question is why is this so??? 2) if instead two electron if we take one positron and one electron then also total wave function become zero when they are in same position. So why positron electron wave function is allowed and while electron electron wave function is not???
Please please reply lol. I need this answer so bad for my school assignment haha.
Hello Pritam, let me try to answer two of your questions.
1) When you flip the labels of two particles, such as changing "ab" to "ba", the wave function of the system changes in a predictable way. In the case of fermions, electrons for example, the wave function must change sign when we swap two particles. This is because of the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously as I mention in the video.
To see why swapping two fermions requires a sign change in the wave function, think it this way; consider a two-particle system with wave function ψ(ab), where "a" and "b" represent the positions of the two particles. Swapping the labels of the particles changes the wave function to ψ(ba). The wave function must be antisymmetric with respect to particle exchange, which means that ψ(ab) = -ψ(ba) This makes sure that the probability density remains unchanged under particle exchange.
2) When two electrons are in the same position, the wave function must be antisymmetric due to the Pauli exclusion principle that I explained in the video. Since the total spin of two electrons is always either zero or one, the wave function must be antisymmetric in both cases. This means that the wave function must be zero when the two electrons are in the same position.
However, an electron and a positron can have a symmetric wave function if their spins combine to form a total spin of zero. What I mean is that the wave function can be non-zero when the electron and positron are in the same position, as long as their spins are in the correct configuration.
I hope it helps! Have a great day.
@@docta2985 I responded to the questions. I wish you best with your school assignment and I hope I wasn't late! :)
@@Semispecula Thank you sooo much! I kinda just said that taking the root of "ψ² (a, b) = ψ² (b, a)" to get the wave functions can give you a positive or negative value after exchange. The positive for bosons and the negative for fermions. I hope that will do cuz I already submitted the draft haha
@@Semispecula hi semispecula, thank you very much, for clearing my doubts. Keep making wonderful video like this
I was wondering why on the first energy level there can be max 2 electrons, why not 1 electron?
Thanks!
Great question, well as the lecture video states, electrons can not have the same quantum numbers in the same place. However in the first orbital, we can have maximum 2 electrons with different quantum numbers. If we had three, two of them would be identical and as the lecture video states this can not be so. Hope it answered your question, if not feel free to ask for more elaboration.
@@Semispecula thanks for answering! My question was more about why it cannot have the same quantom numbers? Like, why is there such a rule? How did the scientists find it out?
@@Почемучка-т6в Well, once we have the same quantum numbers, as I talked about in the lecture video, the wave function turns to 0 and that makes having same quantum numbers not possible. The way scientists found out was with the formulation in the video. I hope it helps!
So basically no two electrons can be at same place or elese they are just 1 electeon.if all quantam numbers are same then they are same place whivh is not possible is what i get
Quantum do occupy the same time however the same space is allocated in peramiters of different
A
Alfas
Based and Mathpilled
Fermions satisfy the Pauli Exclusion Principle because fermion identical particle wave functions combine antisymmetrically. And they are antisymmetric because they satisfy the Pauli Exclusion Principle. (ie - a tautology). Bosons do not satisfy the Pauli Exclusion Principle and they have symmetric wave functions. And um... we don't know WHY -- that is just the way the universe works. It is an assumption (sort of like an axiom in mathematics) and no proof is needed because -- it works and is consistent with what we observe in nature. It is turtles all the way down.
Spin-Statistics theorem.
why fermions are antisymmetric in nature????
They are waves and for some unknown reason, when you combine the waves of two of them, the part of the graphic where is more probably to find the particle, its always in different spots, never close to each other, and this fact creates a "false repulsion."
it's a classification. So fermions are antisymmetric by definition.
Now, why there are any antisymmetric particles/fermions in the world at all (instead of, for example, them all being symmetric), I have no idea.
@@sahelanthropusbrensis I'm sorry, I really don't get your comment. Could you try explaining it again in a bit more detail?
no way you are alive lol (jk)
n can't be zero