Derivative of Lx^2+Ly^2+Lz^2 =?

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Discussion Overview

The discussion revolves around the derivative of the expression ##L_x^2 + L_y^2 + L_z^2##, with a focus on its representation in spherical coordinates. Participants explore the mathematical formulation and seek clarification on the problem statement.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the expression for ##L_x## should use ##\cos \phi## instead of ##\cot \phi##, and that ##L_z## has a sign error.
  • One participant expresses difficulty in proceeding with the problem and seeks assistance.
  • Another participant requests clarification on the problem, suggesting that the thread title may not accurately reflect the issue at hand.
  • A later reply confirms the need to express ##L_x^2 + L_y^2 + L_z^2## in spherical coordinates, specifically mentioning the variables ##(\theta, \phi)##.
  • One participant provides a mathematical expression for ##L_z^2##, indicating a method for calculating each term.

Areas of Agreement / Disagreement

Participants have not reached consensus on the correct formulation of the terms involved, and there are multiple competing views regarding the expressions for ##L_x## and ##L_z##. The discussion remains unresolved as participants continue to seek clarification and assistance.

Contextual Notes

There are unresolved issues regarding the assumptions made in the expressions for ##L_x## and ##L_z##, as well as the clarity of the problem statement itself.

rasi
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Thanks for your helpings...
 

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In ##L_x##, it should be ##\cos \phi##, not ##\cot \phi##. ##L_z## has the wrong sign.
 
DrClaude said:
In ##L_x##, it should be ##\cos \phi##, not ##\cot \phi##. ##L_z## has the wrong sign.

So how can i go on. In no way i coulnd't tackled it. Thanks for your help...
 
rasi said:
So how can i go on. In no way i coulnd't tackled it. Thanks for your help...
Not sure what you mean here.

Can you describe the problem you want to solve? The title of the thread is not very clear, do you mean you need to write ##L_x^2 + L_y^2 + L_z^2## in spherical coordinates ##(\theta, \phi)##?
 
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DrClaude said:
Not sure what you mean here.

Can you describe the problem you want to solve? The title of the thread is not very clear, do you mean you need to write ##L_x^2 + L_y^2 + L_z^2## in spherical coordinates ##(\theta, \phi)##?

yes. just as you said.
 
Then you need to calculate each term by applying it to itself, e.g.,
$$
L_z^2 = L_z L_z = -i \hbar \frac{\partial}{\partial \phi} \left( -i \hbar \frac{\partial}{\partial \phi} \right)
$$
 

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