Division of phase space into elementary cells | Statistical mechanics.
The volume available in phase space can be divided into a large number of compartments. Each compartment is further divided into a large number of elementary cells, each of equal volume. Let d³r = dx dy dz and d³p = dp(x) dp(y) dp(z) be the volume of the element enclosed by a particle cell in position space and momentum space respectively. Then the volume of the element enclosed by the cell in phase space (or mu space) is given by
d(tau) = d³r d³p = ho
In classical mechanics there is no restriction on the choice of ho.
However, in quantum mechanics, the value of ho cannot be made as small as possible. This is because, in quantum mechanics, the uncertainty principle imposes the restriction on the accuracy of the measurement of position and momentum of a particle measured simultaneously.
In this video the total number of elementary cells (or number of quantum states) in phase space are given.
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