Uploaded October 2019 | Updated September 2026, 3 days ago

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In this video, I show you how to derive the angular momentum operator algebra, and a clever way to derive the eigenvalue relations.

My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy

One fact that might help with understanding:
Each representation (position, momentum, etc.) of a given abstract solution of the quantum commutation relations defining a particular set of operators, is itself a distinct solution.

Another fact that might help with understanding:
While every solution to a set of quantum commutators is perfectly usable in quantum mechanics, not every solution represents the same thing. For example, both spin and orbital angular momentum are described by operators that satisfy the angular momentum operator algebra, but different solutions are required for each of them. The harmonic oscillator solution that I showed is a nonspecific abstract solution.

The Generalized Heisenberg Uncertainty Principle:
youtube.com/watch?v=YnR5lacrCqc

The Momentum Operator From The x-p quantum commutator
youtube.com/watch?v=1raxOPuRQPw

Solving The Schrodinger Equation For The Quantum Harmonic Oscillator Using The Ladder Operator Method:
youtube.com/watch?v=PKvePIgQjMg

Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ

Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou