ChemistryAngular momentumUniversity
Angular momentum operator Calculator
Defines orbital angular momentum as the cross product of position and momentum operators.
Use the free calculatorCheck the variablesOpen the advanced solver
Formula first
Overview
This operator measures rotational motion and generates the angular quantum numbers used in atomic orbitals and rigid rotors.
Apply it well
When To Use
When to use: Defines orbital angular momentum as the cross product of position and momentum operators.
Why it matters: This operator measures rotational motion and generates the angular quantum numbers used in atomic orbitals and rigid rotors.
Avoid these traps
Common Mistakes
- Treating L as ordinary scalar momentum.
- Forgetting that components of L do not all commute.
One free problem
Practice Problem
What two operators are crossed to form orbital angular momentum?
Solve for: $\hat{\mathbf{L}}
Hint: Focus on what the formula is telling you physically.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Chemistry LibreTexts, Rotational Motions of Rigid Molecules; Chemistry LibreTexts, Selection Rule for the Rigid Rotator
- Chemistry LibreTexts, Rotational Motions of Rigid Molecules
- Chemistry LibreTexts, Selection Rule for the Rigid Rotator
- NIST CODATA
- IUPAC Gold Book
- Quantum Mechanics (Griffiths)
- Introduction to Quantum Mechanics (Liboff)
- Griffiths, David J. Introduction to Quantum Mechanics. 3rd ed., Cambridge University Press, 2018.