Is the Commutator [P², Lx] in Quantum Mechanics Zero?

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Homework Help Overview

The discussion revolves around the calculation of the commutator [P², Lx] in the context of quantum mechanics. The original poster presents their attempt at solving the problem, which involves the momentum operators and angular momentum operators.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are examining the original poster's approach to calculating the commutator and questioning the accuracy of the commutation relations used. There is a focus on clarifying the question and ensuring that the relevant equations are correctly applied in the solution.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempts and encouraging further clarification of the question. There is no explicit consensus on the correctness of the original attempt, and multiple interpretations of the problem are being explored.

Contextual Notes

The original poster references a specific exercise from a textbook, indicating that the problem is part of a structured learning context. There are mentions of typos in the equations that may affect the understanding of the problem.

gfxroad
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Homework Statement


Calculate the commutative
[P2,Lx]

Homework Equations


P2=P2x+P2y+P2z
[Py,Lx]=-iħPz
[Pz,Lx]=iħPy
[Px,Lx]=[Py,Ly]=[Pz,Lz]=0

The Attempt at a Solution


[P2,Lx]=[P2x+P2y+P2z,Lx]
=[P2x,Lx]+[P2y,Lx]+[P2z,Lx]
=Px[Px,Lx]+[Px,Lx]Px+Py[Py,Lx]+[Py,Lx]Py+Pz[Pz,Lx]+[Pz,Lx]Pz
=-iħ[Py+Py]+iħ[Pz+Pz]
=iħ[P2z+P2y]
 
Last edited:
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First off, what is your question? Second off, your commutation relations are wrong. For example, [P2,L1]=-iħP3.
 
Thanks, I was edited the given (miss-writing)
The question is written in the first step
Calculate the commutative [P^2,Lx]=?
 
Yes, but what is the question you have about how to do this? You've fixed the typo, but you haven't applied the changes to your solution.
 
Last edited:
Please, I want to clear to me is the attempts is wrong or true.
Its an exercise (5.2) page 325 of Quantum Mechanic 2nd edition of Nouredine Zettili. The following is the link of the book.
https://ia601700.us.archive.org/6/items/QuantumMechanicsConceptsAndApplications2ndEdNouredineZettili/Quantum%20Mechanics%20-%20Concepts%20and%20Applications%20-%202ndEd%20-%20Nouredine%20Zettili.pdf
 
As I said before, you've fixed the typos in your "Relevant Equations", but you haven't applied these changes to your solution.
 
tman12321
I was putted the relevant equation directly at the attempt part in the third step of solution.
 
Last edited:

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