3D isotropic quantum harmonic oscillator: power series solution

Опубликовано: 05 Июнь 2026
на канале: Professor M does Science

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📝 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 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
1:47 3D isotropic quantum harmonic oscillator as a central potential
8:18 Radial equation solution
36:22 Wrap-up

⏮️ BACKGROUND
1D quantum harmonic oscillator:    • The quantum harmonic oscillator
3D quantum harmonic oscillator in Cartesian coordinates:    • The 3D 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?
3D isotropic quantum harmonic oscillator | eigenvalues and eigenstates:    • 3D isotropic quantum harmonic oscillator: ...

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Director and writer: BM
Producer and designer: MC