What do the terms in Heisenberg's matrices represent?

[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

 

[werner heisenberg]

Well I see it is not an easy question to answer... Thanks anyway.

 

[Galileo]

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: A_{ii}=\langle \varphi_i|A|\varphi_i \rangle resemble expectation values. It is the expectation value \langle A \rangle of A for a system in the state |\varphi_i \rangle. I don't know of any physical interpretation of the non-diagonal elements.

 

[inha]

uh.. shouldn't you know this stuff pretty well Werner?

 

[werner heisenberg]

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