Professor M does Science | Hydrogen atom: power series solution @ProfessorMdoesScience | Uploaded March 2022 | Updated October 2024, 1 hour ago.
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📚 The hydrogen atom can be described using a Hamiltonian of a central potential. In this video, we go over the mathematical solution of the eigenvalue equation of the Hamiltonian. This requires the solution of a complex differential equation, and involves interesting concepts such as limiting behaviors and power series expansions.

0:00 Intro
1:00 Hydrogen as a central potential
7:27 Radial equation
9:46 Bound vs unbound states
12:52 Simplifying notation
16:38 Radial equation solution
33:07 Quantized energy eigenvalues
39:56 Energy eigenfunctions
45:47 Wrap-up

⏮️ BACKGROUND
Hydrogen atom basics: youtu.be/lndTguV0u1g
3D quantum harmonic oscillator: youtu.be/jOQThICjLlw
Central potentials: youtu.be/Y73ctxnP9gQ
Radial equation of central potentials: youtu.be/MsZP7yxpeFg
Orbital angular momentum: youtu.be/EyGJ3JE9CgE
Spherical harmonics: youtu.be/5PMqf3Hj-Aw
Bound vs unbound states: [COMING SOON]

⏭️ WHAT NEXT?
Hydrogen atom | Eigenvalues and eigenfunctions: youtu.be/T78NkndaMb8
Hydrogen atom | Ground state: youtu.be/r_C82Y6XNWY
Hydrogen atom | Energy spectrum: youtu.be/GV2CDZD2xNk
Hydrogen atom | Spectral series: youtu.be/XawP16g7dJ8

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Director and writer: BM
Producer and designer: MC