Just a quick confirmation-possible angular momentum states of rotator.

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SUMMARY

The discussion revolves around the calculation of possible angular momentum states of a rotator using wavefunctions expressed in spherical harmonics. The user seeks clarification on whether the wavefunction alone represents the possible states or if it should be multiplied by the eigenvalue of Lz. Additionally, the user inquires about the correct method for calculating probabilities, specifically whether to integrate the entire wavefunction squared or just the front coefficient squared. The user has already completed their homework but is looking for confirmation on these points.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically angular momentum.
  • Familiarity with wavefunctions and their normalization.
  • Knowledge of spherical harmonics and their applications in quantum systems.
  • Basic grasp of eigenvalues and their significance in quantum mechanics.
NEXT STEPS
  • Study the role of eigenvalues in quantum mechanics, focusing on Lz and angular momentum.
  • Learn about the normalization of wavefunctions in quantum mechanics.
  • Explore the integration of wavefunctions for probability calculations in quantum systems.
  • Review the properties and applications of spherical harmonics in quantum mechanics.
USEFUL FOR

This discussion is beneficial for students of quantum mechanics, particularly those studying angular momentum, as well as educators and anyone involved in teaching or learning about wavefunctions and their applications in quantum systems.

intelwanderer
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Homework Statement



Wow, the site looks way different from when I was last here. Nice job to whoever did this!

Now, to business...

My question pertains to part 2a of the HW. I've gotten the wavefunction in terms of the spherical harmonics, but I need help bringing it on home, so to speak. My question are pretty stupid actually. When you get the wavefunction(it's already normalized, or so I think), is the possible states just that-the wavefunction, or do you multiply by the eigenvalue of Lz? And the probabilities... do you integrate the whole wavefunction squared with the spherical harmonics, or just the front coefficient squared?

Thank you for your time.


https://courses.utexas.edu/bbcswebdav/pid-5341865-dt-content-rid-23947515_1/courses/2013_spring_58640_PHY_373/hmwrk7.pdf


Homework Equations


Irrelevent.


The Attempt at a Solution



I have the answers to each case already, I just need to know which case is right. I'm probably being overly paranoid, but...
 
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Well, it doesn't really matter now anyway, I turned in the homework several hours ago.
 

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