Manipulate Commutator Relations in Quantum Mechanics - Help Needed

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SUMMARY

This discussion focuses on the manipulation of commutator relations in quantum mechanics, specifically addressing the expression [AB,C]. The user seeks clarity on when it is valid to express this as A[B,C] or A[B,C] + [B,C]A. The product rule analogy in differentiation is highlighted, with the correct relation being [AB,C] = [A,C]B + A[B,C]. The lack of comprehensive resources on this topic is noted, particularly in relation to Griffiths' textbook.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with commutator notation and properties
  • Basic knowledge of differentiation and product rules
  • Access to Griffiths' "Introduction to Quantum Mechanics" textbook
NEXT STEPS
  • Research the properties of commutators in quantum mechanics
  • Study the derivation of the product rule for commutators
  • Explore advanced quantum mechanics textbooks for deeper insights
  • Look into online resources or lectures specifically addressing commutator relations
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Quantum mechanics students, physicists, and researchers seeking to deepen their understanding of commutator relations and their applications in quantum theory.

Dishsoap
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This is not a homework question, I just can't find a good resource on this topic.

I am working in quantum mechanics on commutator relations. My book (Griffiths) lacks information on how to manipulate the commutator relations.

For instance, when I have [AB,C], when can I make it A[B,C]? Or is it A[B,C]+[B,C]A? I can't find an online resource that explains these things. Help please!
 
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samnorris93 said:
This is not a homework question, I just can't find a good resource on this topic.

I am working in quantum mechanics on commutator relations. My book (Griffiths) lacks information on how to manipulate the commutator relations.

For instance, when I have [AB,C], when can I make it A[B,C]? Or is it A[B,C]+[B,C]A? I can't find an online resource that explains these things. Help please!

Do things like the product rule in differentiation:

[AB,C] = [A,C]B + A[B,C]
 

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