How to derive Nielsen equation from Lagrange equation?

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SUMMARY

The discussion focuses on deriving the Nielsen equation from the Lagrange equation, highlighting challenges in understanding the commutator's role in the derivation. Participants reference the Poisson bracket commutator and express confusion over specific relationships within the equations. The conversation emphasizes the need for clarity on the notation and relationships involved in the derivation process.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with commutators in quantum mechanics
  • Knowledge of the Nielsen equation
  • Basic grasp of Poisson brackets
NEXT STEPS
  • Study the derivation of the Nielsen equation in detail
  • Learn about the properties and applications of commutators in quantum mechanics
  • Explore the relationship between Lagrangian mechanics and quantum mechanics
  • Research the significance of Poisson brackets in classical mechanics
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Students and researchers in theoretical physics, particularly those focusing on classical mechanics and quantum mechanics, will benefit from this discussion.

AlephClo
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How to derive Nielsen equation from Lagrange equation
 
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Isn't google your friend ? What did you find so far ?
 
I have done couple hours of research and tried to derive it myself. The best that I found is this, but I do not understand where the commutator come from. It does not seem to be the Poisson braket commutator applied to T either (A,B) = AB-BA . Nor that I understand where the (2) relationship comes from. Thank you

upload_2019-1-9_5-4-47.png
 

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AlephClo said:
The best that I found is this
It was the first one I found too. But: Not good enough then, ... (*)
What about the second one in the list I got ?

:smile: Except where it says ##=0## one should read ## = Q_j##

(*) And yes, the commutator [A,B] means: first B then A minus first A then B.
 
Thank you BvU.
 

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