What do the terms in Heisenberg's matrices represent?

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    Heisenberg Matrices
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Discussion Overview

The discussion revolves around the interpretation of the terms in Heisenberg's matrices, particularly focusing on their meaning within the context of quantum mechanics. Participants explore the significance of diagonal and non-diagonal elements in relation to observables and expectation values.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses uncertainty about the meaning of each term in Heisenberg's matrices and requests a plain language explanation.
  • Another participant suggests that the diagonal elements of a matrix corresponding to an observable resemble expectation values, specifically noting that they represent the expectation value of an observable for a system in a given state.
  • The same participant admits a lack of understanding regarding the physical interpretation of the non-diagonal elements of the matrix.
  • A later reply questions the expertise of the participant who provided the explanation, implying that they should have a better grasp of the topic.
  • Another participant reflects on the complexity of Heisenberg's work, noting that while his uncertainty principle appears straightforward, his broader contributions are often difficult to comprehend.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express varying levels of understanding and uncertainty regarding the interpretation of the matrix terms.

Contextual Notes

Participants acknowledge the complexity of Heisenberg's work and the challenges in interpreting his contributions, indicating that there may be missing assumptions or definitions that complicate the discussion.

werner heisenberg
I was just thinking about what does every one of the terms in Heisenberg's matrices stands for so I decied to post a new thread in physicsforums since I am sure I will obtain an answer before long. Thanks an try to explain it in plain languaje (if possible) because I am not an expert
 
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Well I see it is not an easy question to answer... Thanks anyway.
 
I'm not sure if this is what you're asking, but..
The diagonal elements of some matrix A corresponding to an observable in some orthormal basis: [itex]A_{ii}=\langle \varphi_i|A|\varphi_i \rangle[/itex] resemble expectation values. It is the expectation value [itex]\langle A \rangle[/itex] of A for a system in the state [itex]|\varphi_i \rangle[/itex]. I don't know of any physical interpretation of the non-diagonal elements.
 
uh.. shouldn't you know this stuff pretty well Werner?
 
Yep I should but you see... At first Werner seems rather easy and amazing with its uncertainty principle but when reading its life (David Cassidy Uncertainty, the life and science of werner Heisenberg) you realize this is not true, he published a great deal of papers on a great deal of fields and he is often impossible to understand
 

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