Consider a two state system we studied in quantum mechanics. One example is a S
ID: 1651655 • Letter: C
Question
Consider a two state system we studied in quantum mechanics. One example is a S = 1/2 system, where the spin eigenstates are |+) (pointing upward) and |-) (downward). Now you have 10 of these S = 1/2 particles (they are indistinguishable) and each is allowed to be either in the up (|+)) or down(|-)) state. (a) How many possible spin configurations can we have with these 10 particles? (b) What is the probability that all 10 particles points the same direction? (c) What is the probability that 5 of them are in one direction and the rest are in the other ?Explanation / Answer
From the given question,
Each state has two possibilities.
a) 10 particles can have 210 = 1024 possible configurations.
b)There are only two states when all particles points the same direction. Either all pointing upwards or all pointing downwards.
Hence, probability that all 10 particles point in same direction is 2/1024= 1/512
c)5 of them are up and remaining 5 are down
probability= 10C5 (1/2)5(1/2)5
=[10!/(5!*5!)]/1024
=252/1024
=63/256
The probability that 5 of them are in one direction and rest in other is 63/256