 #1
tanaygupta2000
 204
 14
 Homework Statement:

Three bosons are to be filled in two energy states with degeneracies 3 and 4 respectively.
(1.) List all the macrostates.
(2.) How many microstates does this 3particle system has?
(3.) Which macrostate is the most probable one?
 Relevant Equations:
 Partition function, Z = ∑g(j)exp(E(j)/kT)
Upto now I've only dealt with the problems regarding non  degenerate energy states.
Since bosons do not follow Pauli's Exclusion Principle, three bosons can be filled in two energy states (say E_{1} and E_{2}) as:
so that there are 2 macrostates (corresponding to levels E_{1} and E_{2}) and 4 microstates (corresponding to 4 possibilities).
Also the probability of occurrence of
I do not understand the meaning behind the given degeneracies of energy states.
Since bosons do not follow Pauli's Exclusion Principle, three bosons can be filled in two energy states (say E_{1} and E_{2}) as:
E_{1}  E_{2} 
1 boson  2 bosons 
2 bosons  1 boson 
3 bosons  0 bosons 
0 bosons  3 bosons 
so that there are 2 macrostates (corresponding to levels E_{1} and E_{2}) and 4 microstates (corresponding to 4 possibilities).
Also the probability of occurrence of
 I Possibility = 3!/2! = 3
 II Possibility = 3!/2! = 3
 III Possibility = 3!/3! = 1
 IV Possibility = 3!/0! = 6
I do not understand the meaning behind the given degeneracies of energy states.