Professor M does Science | The radial equation of central potentials @ProfessorMdoesScience | Uploaded May 2021 | Updated October 2024, 2 hours ago.
How can we describe the radial motion of a quantum particle moving in a central potential?

📚 A central potential is a potential that only depends on the distance from the origin, but does not depend on the orientation about the origin. This means that the motion of a particle moving in a central potential can be separated into its radial and angular parts. The angular part is fully determined by the equations of orbital angular momentum in quantum mechanics. In this video we explore the equation obeyed by the radial part. We also discuss the related and important concept of an effective potential.

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⏮️ BACKGROUND
Central potentials: youtu.be/Y73ctxnP9gQ
Orbital angular momentum: youtu.be/EyGJ3JE9CgE
Orbital angular momentum eigenvalues: youtu.be/5h5mbL5rco0
Orbital angular momentum eigenfunctions: youtu.be/Gk2XNmIHVwo
Position representation: youtu.be/Yw2YrTLSq5U

⏭️ WHAT NEXT?
3D harmonic oscillator: [COMING SOON]
Hydrogen atom: [COMING SOON]

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Director and writer: BM
Producer and designer: MC