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Ken G
Mar8-12, 09:02 AM
PF Gold
P: 3,136
Quote Quote by A. Neumaier View Post
If the environment consists of different particles than the single molecule, the situation is similar, even if the molecule is as heavy or heavier than the particles in the environment.
That cannot be true about that paper, because it uses an expansion in a "small parameter" relating to the mass ratio. If the mass ratio is unity, their approach does not achieve its objective.
But a water molecule surrounded by water is different as the different water molecules are indistinguishable. (A practical question is: How does one remember which molecule was singled out, as all are indistinguishable?)
Yes, indistinguishability would be an interesting wrinkle to an exercise like that, it would interesting if it mattered in some way as to how that "cut" comes about!
In any case, the answer is here given by the 1-particle reduced density operator of statistical mechanics (if the water molecule is considered as asingle particle). See. e.g., Chapter 7F of Reichl's book on statistical Physics.
If they are looking for a mathematical answer, then yes, that would be a good way to go. If they are looking for a physical description of what is going on, or if they don't have that text handy, then other kinds of answers could be useful, perhaps along the lines of those given above.