Question

1 More State Counting Consider a system with 2 N-state systems, with $N gg 1$. For example, for the case where $N = 2$, you could imagine two spin 1/2 particles, or for a case with $N = 100$, two particles in a 1-D harmonic oscillator but confined to the lowest 100 levels. The point is you have only two particles, but they can fill up to $N$ levels. The system is assumed to be warm compared to $Delta E$, so all states are occupied equally. (a) What is the probability for finding the particles in the same state if they are distin- guishable? (b) What is the probability for finding the particles in the same state if they are fermions? (c) What is the probability for finding the particles in the same state if they are bosons?

          1 More State Counting
Consider a system with 2 N-state systems, with $N gg 1$. For example, for the case where
$N = 2$, you could imagine two spin 1/2 particles, or for a case with $N = 100$, two particles
in a 1-D harmonic oscillator but confined to the lowest 100 levels. The point is you have
only two particles, but they can fill up to $N$ levels. The system is assumed to be warm
compared to $Delta E$, so all states are occupied equally.
(a) What is the probability for finding the particles in the same state if they are distin-
guishable?
(b) What is the probability for finding the particles in the same state if they are fermions?
(c) What is the probability for finding the particles in the same state if they are bosons?

1 More State Counting
Consider a system with 2 N-state systems, with N gg 1. For example, for the case where
N = 2, you could imagine two spin 1/2 particles, or for a case with N = 100, two particles
in a 1-D harmonic oscillator but confined to the lowest 100 levels. The point is you have
only two particles, but they can fill up to N levels. The system is assumed to be warm
compared to Delta E, so all states are occupied equally.
(a) What is the probability for finding the particles in the same state if they are distin-
guishable?
(b) What is the probability for finding the particles in the same state if they are fermions?
(c) What is the probability for finding the particles in the same state if they are bosons?

Added by Mariano A.

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