Angular Momentum Expectation Values help for noobie

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SUMMARY

The discussion focuses on calculating the expectation values + for a particle in the quantum state Y(l=3, m=+2). A key formula provided is L_x^2 + L_y^2 = L^2 - L_z^2, which simplifies the calculation. The brute force method of computing integrals is mentioned but not recommended. This highlights the importance of utilizing established quantum mechanics principles for efficient problem-solving.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically angular momentum.
  • Familiarity with spherical harmonics, particularly Y(l, m) functions.
  • Knowledge of expectation values in quantum mechanics.
  • Basic skills in integral calculus for evaluating quantum integrals.
NEXT STEPS
  • Study the derivation and applications of the angular momentum operators L_x, L_y, and L_z.
  • Learn about the properties and normalization of spherical harmonics Y(l, m).
  • Explore the concept of expectation values in quantum mechanics in greater depth.
  • Investigate alternative methods for calculating quantum mechanical integrals.
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics and angular momentum calculations, will benefit from this discussion.

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For a particle in the state Y(l=3, m=+2), how do I find <Lx^2> + <Ly^2> ? I'm lost. THanks!
 
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1) You can do it by brute force - compute the relevant integrals (I don't advocate this method).

2) Consider the following useful fact:

[tex]L_x^2+L_y^2=L^2-L_z^2[/tex]
 

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