Description of Microstate

Within the quantum mechanical description, only certain discreet values of molecular states are allowed. A single molecule or a particle in a cubic box of volume V and side a =V^0.33 can only have values of energy given by:

Here a_x,a_y and a_z can take values which are integers such as 0,1,2,3…etc. m here is the particle mass and h is the Planck’s constant. We have reached to point where it is necessary to define particle energy level and energy state. A specification of the quantum ctate i.e the values ofa_x,a_y and a_z  makes up the energy state. For e.g the three energy states may be (1,2,2),(2,1,2) and (2,2,1).All the energy states will have the same energy level i.e:

Thus the above case is an example of threefold degenerate i.e the particle having three energy states having the same energy level.

So far we have seen our discussion mainly based on single particle system. However important lies in the energy states of a large assembly of non-interaction molecules. Also let us assume that the molecules are indistinguishable. So a energy state is merely a set of occupation number such as n=(n1,n2,n3…..) ,where ni is the number of molecules in the i ^th molecular state. Every distinct energy state will now be given a set of occupation numbers. So the ith energy state will be specified by the vector  .Here  is the occupation number of the j ^th single molecule energy state in the i ^th energy state of the assembly. So every  represents a distinct microstate of the system and is given by: