Central potentials in quantum mechanics

How can we study a particle moving in a central potential in quantum mechanics?

📚 A central potential is a potential that only depends on the distance from the origin, but does not depend on the orientation about the origin. Central potentials feature in a range of physical system, from the 3-dimensional isotropic harmonic oscillator, to the relative motion of the electron and proton in a hydrogen atom. In this video we introduce central potentials and show how they are related to orbital angular momentum.

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⏮️ BACKGROUND
Orbital angular momentum:    • Orbital angular momentum in quantum mechanics  
Orbital angular momentum eigenvalues:    • Orbital angular momentum eigenvalues  
Orbital angular momentum eigenfunctions:    • Orbital angular momentum eigenfunctions  
Position representation:    • Position and momentum operators acting on ...  
Constants of motion:    • Constants of motion in quantum mechanics  

⏭️ WHAT NEXT?
Central potentials | Radial equation:    • The radial equation of central potentials  
3D harmonic oscillator: [COMING SOON]
Hydrogen atom: [COMING SOON]

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Director and writer: BM
Producer and designer: MC