Hydrogen atom: power series solution
📚 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: • The hydrogen atom
3D quantum harmonic oscillator: • 3D isotropic quantum harmonic oscillator: ...
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
Bound vs unbound states: [COMING SOON]
⏭️ WHAT NEXT?
Hydrogen atom | Eigenvalues and eigenfunctions: • Hydrogen atom: eigenvalues and eigenfuctions
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