Statistical effect of localized quantum objects

Let us consider an ensemble of N localized, and hence discernible, molecules, such that its volume V, total energy E and the number N remain constant. In a given state, each molecule has an energy e with the states being degenerated g, times. We often call this collection a microcanonical ensemble. We can therefore write  

We will find that, in the same case as in section 4.2, the number of ways om N elements can be arranged in the space of phases is given by an expression in the same form as inequality [4.6] where we can now assume that each energy level has several corresponding states g, for. The probability is therefore mirltiplied by g, the same for each element, and for 

This is the same Maxwell-Boltzmann statistic and we can therefore write = gi exp (-a) exp ) [4.45] 

The coefficient P has the same value as above (see section 4.7) and the coefficient a is deduced in a similar way to equation [4.12] by  

- The sum that appears in the denominator in expressions [4.47] and [4.48] is called the molecular partition Junction, defined by  

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