- #1

- 1,434

- 2

**What is the definition of "particle(s)" in QM?**

Hello,

It is said that "identical particles are indistinguishable", but I'm beginning to think such a weird sentence is only a result of butchering the word "particle". More concretely: what is actually

*meant*with the word "particle" in the QM formalism?

"One particle", I suppose, can be defined as "a solution of the regular three-dimensional Schrödinger equation". Would someone agree? To go on, one can then define a certain experimental apparatus (defining in the sense of building it) and define position as what is measured by it and postulate [itex]|\psi(\textbf r)|^2[/itex] as the distribution of this "position".

Then for the definition of "particle

__s__": analogously one can define "a system of n identical particles" as a solution of

[tex]i \hbar \frac{\partial}{\partial t} \psi(\textbf r_1, \dots, \textbf r_n) = \left( - \sum_{i=1}^n \frac{\hbar^2}{2m} \nabla_i^2 + V(\textbf r_1, \dots, \textbf r_n) \right) \psi(\textbf r_1, \dots, \textbf r_n)[/tex]

but from then on I'm not sure what to do. Should we again define position from scratch operationally? Or should it somehow relegate back to the one-particle case? Or is the measuring apparatus somehow taking into account all the n "particles" at the same time? Isn't a "n particle system position measuring apparatus" simply the measuring apparatus for the one particle case multiplied by n?

Basically, what I'm struggling with is knowing what meaning to give to a "n particle system", while sentences like "identical particles are indistinguishable" already presume everything is well-defined, as if the one particle case said everything you needed to know (which was the case in classical mechanics, anyway).

I hope there are some out there who understand what I am getting at. If not, then let me simply ask: what do

*you*understand under "a system of n (identical) particles"?