Quantum Chemistry 7.1 - Hydrogen Atom Model

Short lecture on the hydrogen atom in quantum mechanics.

The hydrogen atom quantum mechanical model system has a proton fixed at the origin and an electron which can move anywhere in 3 dimensions. The Hamiltonian operator is the kinetic energy of the electron plus the potential energy of the electron's attraction to the nucleus / proton. The potential energy depends only on the electron's distance from the nucleus, thus we express the Hamiltonian and the wavefunction in terms of spherical polar coordinates. The potential energy function is the product of the charge of the electron and proton divided by [ 4 pi epsilon_nought r], where r is the electron's distance from the proton / origin.

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[neemo]

thank you very much. i was very intimidated looking at my textbook on the hydrogen atom. the laplacian operator really scared me but then i realized it's just being re-expressed in spherical coordinates

[oluagwu]

Thanks Q - Chem this is very helpful and educational

[whosyourdaddy]

thank you so much!!!, really helped me a lot. I hope my Professor is straightforward like this.

[ananyapassi]

BEST CHANNEL FOR QUANTUM CHEMISTRY :-) !!! Can someone please tell me how this Laplacian was derived?

[minniemay]

I think the last term in the laplacian should be 1/(r^2*sin^2(theta)) * partial phi

[aaronbell]

I want to watch the rest of this. I am familiar with these axioms. I can't seem to get to the rest of the lecture. I will continue to try and do it. So far, I know exactly what the prof is speaking about. I want to watch the progression, but this appears to be the end. I can't seem to find the rest of the lecture. I guess it's not pop. I will keep trying. Please do not censor info based on its info value in the general population. I want to see this in its entirety. That would be great.

[TheFlameGarden]

I might be crazy but i think i saw hydrogen atoms with my eyes when they focused in a funky way. I saw 4 or 5 rings two dots on either side. They all more or less seemed aligned with one another too as they sit on my arm. I believe they really were atoms because my skin slowly began absorbing them.