Angular momentum magnitude commutator Calculator

Formula first

Overview

This is why quantum states can be labeled by both l and one component quantum number m.

Apply it well

When To Use

When to use: Shows that any one angular-momentum component commutes with the total squared angular momentum.

Why it matters: This is why quantum states can be labeled by both l and one component quantum number m.

Avoid these traps

Common Mistakes

• Confusing this with the nonzero commutator between different components.
• Thinking all three components commute because each commutes with $L^2$.

One free problem

Practice Problem

Can $L^2$ and Lz have simultaneous eigenfunctions?

Solve for: $[\hat{L}_i, \hat{L}^2]

Hint: Focus on what the formula is telling you physically.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Chemistry LibreTexts, Rotational Motions of Rigid Molecules; Chemistry LibreTexts, Selection Rule for the Rigid Rotator
2. Chemistry LibreTexts, Rotational Motions of Rigid Molecules
3. Chemistry LibreTexts, Selection Rule for the Rigid Rotator
4. Griffiths, David J. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.
5. Sakurai, J. J., & Napolitano, Jim. (2017). Modern Quantum Mechanics (2nd ed.). Cambridge University Press.
6. Griffiths, David J. Introduction to Quantum Mechanics
7. Sakurai, J. J., & Napolitano, J. Modern Quantum Mechanics