Electron Spin and the Pauli Principle

[@mariaph9700]

You should record your lectures more often. They are clear and concise. Thank you for sharing!

[@nikhilderreine2910]

very well explained and clearly pronounced. Even beeing german i have no probs understanding you Sir. Thanks! Contine this great work pls. Greetings

[@malaydalui]

Excellent presentation !!

[@EdwinGonzalez-vs9el]

Fantastic class. Greetings from argentina

[@edgarskletnieks5836]

Awesome stuff !

[@Sara_tarawneh]

Thank you so much, How can I get videos related to hydrogen atom ?

[@masifchemist3]

Sir it is very helpful. Thanks

[@suryanshkashyap8925]

Could you please also discuss valence bond treatment .

[@julianfierro5832]

genio capo titan maestro maquina

[@soumyaranjanthakur7652]

Your explanation is the best ....from other you tuber ...so can you upload your class video for us like some important chapter Like some spectroscopy , group theory ,organic reaction mechanism ,thermodynamics .....please sir....please spred your knowledge ...for us ..books have language but not understable always ...thanks you

[@ishfaqwani9216]

Where r ur other lectures sir

[@SonuNigamUnofficial]

U r freqently refering to ur previos lectures...but i cant find them in ur channel...are those being removed sir?? Apart from this U r a teacher who teaches science like a story thank u sir

[@TDanielCrawfordVT]

I created this lecture for my class when I had to travel. The reference to other lectures is to other in-class presentations, not KZbin videos, I’m afraid.

[@岡安一壽-g2y]

Hello, sir ! The anti-symmetric wave function is not the eigenfunction and does not lead us the total energy. For example, please suppose the case Electron 1 is in a hydrogen atom and Electron 2 is in a helium ion He+. And the atom and the ion are far enough. The anti-symmetric wave function of the two electrons is not the eigenfunction of the system. Please calculate it. It is very easy.

[@TDanielCrawford]

Can you clarify your comment? For an electronic wave function, the Pauli principle explains that the exact wave must be antisymmetric, regardless of the distance between the nuclei. A single-determinant wave function is most certainly not the eigenfunction of the corresponding two-electron system you describe, and I never suggested otherwise. The variationally optimized single-determinant anti-symmetric wave function (i.e. the Hartree-Fock wave function) is merely an approximation. Perhaps I don't follow your larger point.

[@岡安一壽-g2y]

Mr.@@TDanielCrawford Thank you for your answer. Now, I'll explain the example. Electron 1 is in a hydrogen atom. Electron 2 is in a helium ion He+. rA, rB:the position of each nucleus. ❘rA-rB❘>>1. The interaction between the electrons is weak enough. H1=(p1^2/2m)-(e^2/4πε0❘r1-rA❘), H2=(p2^2/2m)-(2e^2/4πε0❘r2-rB❘), H1φA(r1)=EAφA(r1), H2φB(r2)=EBφB(r2). Hartree product φA(r1)φB(r2) is the eigenfunction of operator H1+H2, and give us the energy of the system EA+EB. But, another product φA(r2)φB(r1) is not the eigenfunction of operator H1+H2. Therefore, the anti-symmetric wave function ψ=φA(r1)φB(r2)-φA(r2)φB(r1) is not the eigenfunction of the system, as you wrote. Please teach me the reason why modern physics adopt the anti-symmetric function as the wave function of the system.

[@TDanielCrawford]

@@岡安一壽-g2y Wave function antisymmetry is a property of all fermionic systems, such as electrons. A result of this antisymmetry is Pauli exclusion, which, in this particular case, implies that no two electrons can occupy the same state (i.e. have the same set of quantum numbers, including spin). Your Hartree product wave function (which also ignores spin) does not provide this property, and thus is not a correct description of an electronic wave function.

[@岡安一壽-g2y]

@@TDanielCrawford I am deeply grateful to you, sir. Generally, the anti-symmetric wave function is not the eigenfunction of the system, as you know. The anti-symmetric function and Hartree product can't show the probability of finding the particle. Therefor, we should prove Pauli exclusion principle by using the other method.

[@岡安一壽-g2y]

@@dipayandatta3540If there is an example that does not apply, it is not a theorem. It is not a theorem that the anti-symmetric wave function is the eigenfunction of the system. As you know, the anti‐symmetric wavefunction can be the eigenfunction of the system only if the Hamiltonian is invariant with the replacement of particles.

[@janjakruso]

goatsın