Ehrenfest Theorem: Deriving Minus Sign in Commutator

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SUMMARY

The discussion centers on the derivation of the minus sign in the commutator [H,A] as presented in G. Frieseke's article on arxiv.org and a related handout on operator theory. The minus sign arises from the presence of the imaginary unit 'i' within the bra vector, which, upon taking the complex conjugate, results in a negative 'i'. This detail is crucial for understanding the behavior of self-adjoint operators in quantum mechanics.

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  • Understanding of quantum mechanics principles, specifically operators and commutators.
  • Familiarity with complex numbers and their conjugates.
  • Knowledge of self-adjoint operators and their significance in quantum theory.
  • Access to academic resources such as G. Frieseke's article and operator theory handouts.
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  • Study the properties of self-adjoint operators in quantum mechanics.
  • Review the mathematical foundations of commutators in quantum theory.
  • Examine the role of complex conjugates in quantum mechanics.
  • Read G. Frieseke's article on arxiv.org for a deeper understanding of the derivation process.
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PineApple2
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Might be trivial, but: In deriving it, I don't understand how the minus sign comes into establish the [H,A] commutator. (it seems to me that both partial derivatives of ψ should come out positive)
For example, in
http://www.tcm.phy.cam.ac.uk/~bds10/aqp/handout_operator.pdf
on page 5.
 
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Search for the G. Frieseke's article on arxiv.org. That's the proof for general self-adjoint operators.
 
Lol, those are my lecture notes.

The minus sign is there because you have the i inside the bra and so when you take its complex conjugate you get a -i.
 
Randomguy said:
Lol, those are my lecture notes.

The minus sign is there because you have the i inside the bra and so when you take its complex conjugate you get a -i.

right... Thanks!
 

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