Hydrogen Atom In A Crystal | Perturbation Theory | Wigner-Eckart Thm.

Uploaded July 2022 | Updated September 2026, 2 days ago

In this video, I calculate the first order correction to the ground and first excited state hydrogen atom energy levels due to the weak coulomb field of a large ion crystal lattice. It is a good degenerate perturbation theory exercise, and a good demonstration of the utility of the Wigner-Eckart theorem in saving a lot of time.

My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy

I suppose I should have draws the 2s orbital bigger.

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$Solving The Schrodinger Equation On A Sphere | Quantum Mechanics In this video, I show you how to solve the Schrodinger equation for a particle confined to a 2-sphere space. My Quantum Mechanics Lecture Series: https://www.youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy There is a typo in the spherical harmonics normalization constant. In the second fraction under the square root, the 1s are supposed to be ls. Deriving The Orbital Angular Momentum Eigenfunctions: https://www.youtube.com/watch?v=CgcCEhbNOMg&feature=youtu.be Superfluid Helium Resonance Experiment video: https://youtu.be/unUNQNmuvUQ Quantum Field Theory Lecture Series: https://www.youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou *I realize that a sphere is technically the surface of a ball, and so saying the surface of a sphere is not technically perfect. *I also realize that the formula for the orbital-angular-momentum-squared operator given at the end should have a prefactor of negative h-bar squared. That formula itself isnt used for anything in the calculation, so this error in no way effects the calculation.$