3D isotropic quantum harmonic oscillator: eigenvalues and eigenstates
📝 Problems+solutions:
Quantum harmonic oscillator I: https://professorm.learnworlds.com/co...
Quantum harmonic oscillator II: https://professorm.learnworlds.com/co...
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📚 The 3D isotropic quantum harmonic oscillator can be described using a Hamiltonian of a central potential. In this video, we explicitly build the first few eigenvalues and eigenstates of this system. The eigenstates are written in terms of spherical harmonics because they are also eigenstates of orbital angular momentum.
0:00 Intro
1:34 3D isotropic quantum harmonic oscillator as a central potential
5:35 Recap of the mathematical solution of the eigenvalue equation
11:46 Ground state
19:58 First excited state
27:22 Second excited state
30:21 Wrap-up
⏮️ BACKGROUND
1D quantum harmonic oscillator: • The quantum harmonic oscillator
3D quantum harmonic oscillator in Cartesian coordinates: • The 3D quantum harmonic oscillator
3D quantum harmonic oscillator in spherical coordinates: • 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
⏭️ WHAT NEXT?
Hydrogen atom: • Hydrogen atom
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Director and writer: BM
Producer and designer: MC