Why do I get to a contradiction?

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    Contradiction
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Discussion Overview

The discussion revolves around a contradiction encountered by a participant while applying angular momentum operators in quantum mechanics, specifically involving the raising operator and its action on eigenstates. The scope includes theoretical aspects of quantum mechanics and mathematical reasoning related to operator algebra.

Discussion Character

  • Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the action of the operator \( L_z L^+ \) on the state \( |m\rangle \) and claims to have reached a contradiction.
  • Another participant seeks clarification on the notation and suggests a possible interpretation involving the eigenstate \( |l,m\rangle \) and the raising operator \( L^+ \).
  • A third participant implies that the initial claim of contradiction indicates an error in the participant's reasoning, although this is not explicitly confirmed.
  • Another participant acknowledges the possibility of misunderstanding the mathematics while maintaining that the original participant may not have made an error.
  • A request is made for the original participant to share their work to better understand the source of the contradiction.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the original participant made an error. There are competing views regarding the understanding of the mathematics involved, and the discussion remains unresolved.

Contextual Notes

The discussion highlights potential ambiguities in notation and the need for clarity in mathematical steps, but these aspects remain unresolved.

Gjmdp
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I don't understand why LzL+ acting over m is Planck constant(m+1) L+|m>. I 've done it and I've got to a contradiction. Am I doing something wrong?
 
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Your notaion is difficult to understand. Do you mean
$$
L_z L^+ | l,m \rangle = \hbar (m+1) L^+ | l,m \rangle
$$
with ##L^+## the raising operator and ##| l,m \rangle## an eigenstate of ##L^2## and ##L_z## (with quantum numbers ##l## and ##m##)?

If so, what is the result of ##L^+ | l,m \rangle##?
 
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Gjmdp said:
I've got to a contradiction. Am I doing something wrong?
Even though you didn't say what exactly have you done, the above is sufficient to conclude that the answer is - yes.
 
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Demystifier said:
Even though you didn't say what exactly have you done, the above is sufficient to conclude that the answer is - yes.
Yup that is very probable. But, there's still the option I didn't understand some of the mathematics, and yet, I may not have done anything wrong.
 
Gjmdp said:
Yup that is very probable. But, there's still the option I didn't understand some of the mathematics, and yet, I may not have done anything wrong.

Then please show us what you have already done.
 

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