Fundamental Postulate Revisited
Statistical Distributions
• 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
321
312
213
231
123
132
411
141
114
3 ways
more likely
6 ways
• 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.