Ehrenfest Theorem: Deriving Minus Sign in Commutator

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Discussion Overview

The discussion revolves around the derivation of the minus sign in the commutator [H,A] as part of the Ehrenfest theorem, focusing on the mathematical details involved in the derivation process. The scope includes theoretical aspects of quantum mechanics and operator algebra.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant expresses confusion about the origin of the minus sign in the commutator [H,A], suggesting that both partial derivatives of ψ should yield positive results.
  • Another participant recommends consulting G. Frieseke's article on arxiv.org, which purportedly provides a proof for general self-adjoint operators.
  • A participant notes that the minus sign arises due to the presence of the imaginary unit i inside the bra, indicating that taking its complex conjugate results in a -i.

Areas of Agreement / Disagreement

There is no consensus on the derivation of the minus sign; participants present differing perspectives and explanations without resolving the initial confusion.

Contextual Notes

Some assumptions regarding the properties of self-adjoint operators and the handling of complex conjugates may not be explicitly stated, which could affect the clarity of the derivation.

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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