Hydrogen atom: eigenvalues and eigenfuctions
📚 The hydrogen atom is one of very few systems for which we can write down analytical expressions for its eigenvalues and eigenfunctions. In this video, we explicitly build the first few eigenvalues and eigenfunctions of the hydrogen atom. The eigenfunctions are written in terms of spherical harmonics because they are also eigenfunctions of orbital angular momentum.
0:00 Intro
0:35 Hydrogen atom as a central potential
4:53 Recap of the mathematical solution of the eigenvalue equation
12:49 Ground state
20:31 First excited state
34:16 Second excited state
37:34 Wrap-up
⏮️ BACKGROUND
Hydrogen atom basics: • The hydrogen atom
Hydrogen atom | Maths: • Hydrogen atom: power series solution
Central potentials: • Central potentials in quantum mechanics
Radial equation of central potentials: • The radial equation of central potentials
Orbital angular momentum: • Orbital angular momentum in quantum mechanics
Spherical harmonics: • The spherical harmonics
⏭️ WHAT NEXT?
Hydrogen atom | Ground state: • The hydrogen atom ground state
Hydrogen atom | Energy spectrum: • The hydrogen atom energy spectrum
Hydrogen atom | Spectral series: • The hydrogen spectral series
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Director and writer: BM
Producer and designer: MC