In a system of particles, each particles can be in any one of three possible quantum states. The ratio of the probability that the two particles occupy the same state to the probability that the two particle occupy different state for B-E statistics is.Correct answer is '1'. Can you explain this answer?

Question

Answer

Probability in B-E statistics

Introduction:
In quantum statistics, particles are classified into two major categories - bosons and fermions. Bosons follow Bose-Einstein (B-E) statistics, while fermions follow Fermi-Dirac statistics. B-E statistics describes the behavior of particles with integer spin, such as photons, while Fermi-Dirac statistics describes the behavior of particles with half-integer spin, such as electrons.

Probability of particles in the same state:
Let's consider a system of two particles that can each be in any one of three possible quantum states. For B-E statistics, any number of particles can occupy the same quantum state. Therefore, the total number of ways in which both particles can occupy the same state is given by:

N(same) = 3 (number of possible states for each particle) * 3 (number of possible states for the other particle) = 9

Probability of particles in different states:
Similarly, the total number of ways in which both particles can occupy different quantum states is given by:

N(different) = 3 (number of possible states for each particle) * 2 (number of possible states for the other particle) = 6

Ratio of probabilities:
The ratio of the probability that the two particles occupy the same state to the probability that they occupy different states is given by:

P(same) / P(different) = N(same) / N(different) = 9 / 6 = 3 / 2

Conclusion:
The ratio of the probability that the two particles occupy the same state to the probability that they occupy different states for B-E statistics is 3/2. Therefore, the correct answer is NOT '1'.

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