Another index notation question hopefully pretty easy

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Discussion Overview

The discussion revolves around understanding the index notation expression r_j r_i p_j and its relationship to the vector expression \vec{r} (\vec{r} \cdot \vec{p}). The context includes considerations of commutativity in the context of quantum mechanics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant seeks to understand how the index notation expression relates to a vector expression and questions the commutativity of the indices.
  • Another participant asserts that the coordinates are simply numbers and therefore commutative.
  • A third participant agrees that the indices can be commuted and shares a personal sentiment about the ease of working with commutative properties after experience with quantum operator calculations.
  • A later reply expresses gratitude and shares a personal perspective on commutativity based on experience with quantum problems.

Areas of Agreement / Disagreement

Participants generally agree that the indices can be commuted, but there is an underlying uncertainty expressed about commutativity in broader contexts, particularly in quantum mechanics.

Contextual Notes

The discussion reflects a reliance on the assumption that the indices represent numerical coordinates, which may not hold in all contexts, especially in quantum mechanics where non-commutativity can arise.

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How do I make sense of the index notation expression

<br /> r_j r_i p_j<br />

?

What I really *want* it to be is

<br /> \vec{r} (\vec{r} \cdot \vec{p})<br />

And it turns into this, as long as I can commute the r_i[/tex] and r_j...right?<br /> <br /> (By the way, here \vec{r} is just the position vector and \vec{p} is the momentum vector.)
 
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Well, those are simply coordinates, i.e. numbers, so they are commutative, aren't they?
 
Yes, you can commute them just fine. I know how you feel, after doing a lot of quantum operator calculations it feels like such a breeze to have the commutative property!
 
Thanks guys! Yes, this is actually something that's come up in trying to solve a quantum problem. And yeah...I've done enough of these to where I pretty much don't believe anything commutes anymore :(
 

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