How can I confirm Lz=ħ,0,-ħ using operators and eigenfunctions?

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Discussion Overview

The discussion revolves around confirming the eigenvalues of the angular momentum operator Lz, specifically for the values ħ, 0, and -ħ, using operators and eigenfunctions in quantum mechanics. The scope includes theoretical aspects of quantum mechanics and the application of spherical harmonics as eigenfunctions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant presents the eigenvalue equation LzYilm(θ,ϕ) = mħYilm(θ,ϕ) and asks for steps to confirm the eigenvalues of Lz.
  • Another participant explains that Ylm are spherical harmonics, which are eigenfunctions of L^2 and Lz, and notes that for l=1, m can take values +1, 0, -1, leading to the possible eigenvalues of -ħ, 0, and ħ.
  • A participant expresses confusion about how to proceed with the confirmation process and requests guidance.
  • Some participants suggest referring to external resources for operators and eigenfunctions related to the topic.

Areas of Agreement / Disagreement

Participants generally agree on the theoretical framework involving the eigenvalue equation and the role of spherical harmonics, but there is no consensus on the specific steps to confirm the eigenvalues, as one participant expresses a lack of understanding.

Contextual Notes

There are limitations in the discussion regarding the clarity of the steps needed to confirm the eigenvalues, as well as the dependence on understanding the definitions and properties of the operators and eigenfunctions involved.

kenyanchemist
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Hi,
I have a question
Given the function
LzYilm(θ,ϕ) =mħYilm(θ,ϕ)
What steps can I take to confirm that
Lz=ħ,0,-ħ
 
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kenyanchemist said:
I have a question
Given the function
LzYilm(θ,ϕ) =mħYilm(θ,ϕ)
What steps can I take to confirm that
Lz=ħ,0,-ħ

you are writing an eigen value equation for the z component of angular momentum operator called Lz
Ylm are spherical harmonics which are eigen functions of L^2 and Lz
if L=1 then m can take values +1, 0, -1 so the possible eigen values will be -h bar, 0, hbar

now you are asking what steps to confirm - then you can write the form of Lz and apply on spherical harmonics with l=1 and see what possible values comes out from eigen value equation.
 
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Umm... how do I go about that?! Please understand am like super new on quantum mechanics
Please show me :cry::cry:
 

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