Fundamental Postulate Revisited

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Presentation transcript:

Fundamental Postulate Revisited

Statistical Distributions (10 huge number particles) As we know, statistical mechanics deals with the behavior of systems of a large number of particles. But, we give up trying to keep track of individual particles. If we can’t solve Schrödinger’s equation in closed form for helium (4 particles) what hope do we have of solving it for the gas molecules in this room? (10 huge number particles) Statistical mechanics handles many particles by calculating the most probable behavior of the system as a whole, rather than by being concerned with the behavior of individual particles.

In statistical mechanics, we assume that the more ways there are to arrange the particles to give a particular distribution of energies, the more probable is that distribution. (Seems reasonable?) 6 units of energy, 3 particles to give it to 6 ways 3 2 1 3 1 2 2 1 3 2 3 1 1 2 3 1 3 2 1 1 4 4 1 1 1 4 1 3 ways more likely

In statistical mechanics, we assume that the more ways there are to arrange the particles to give a particular distribution of energies, the more probable is that distribution. (Seems reasonable?) We begin with an assumption that we believe describes nature. We see if the consequences of the assumption correspond in any way with reality. It is not “bad” to begin with an assumption, as long as we realize what we have done, & discard (or modify) the assumption when it fails to describe things we measure and observe.