Question

We observe 3 particles and 3 different one-particle states
ψ_{a}(x), ψ_{b}(x) i ψ_{c}(x). How many
different states that describe a system of three particles can we
make:

(a) if the particles can be distinguished;

(b) if the particles are identical bosons;

(c) if the particles are identical fermions?

Note that, unlike the exercise task, there is a possibility that the particles may be in the same quantum state.

For example, ψ(x_{1}, x_{2}, x_{3}) =
ψ_{a}(x_{1})ψ_{a}(x_{2})ψ_{c}(x_{3})

Answer #1

Solution:

3 particles and 3 different one-particle states

So here ni =3 , gi =3

(i)Hence ,if the particles can be distinguished then different states that describes a system of three particles we can make is (gi)^ni=3^3=27

(ii)Hence, if the particles are identical bosons , then different states that describe a system of three particles we can make is W= (ni+gi–1)!/{ni!*(gi!–1)} = (3+3–1)!/(3!×2!) =10

(iii) Hence, if the particles are identical fermions , then different states that describes a system of three particles we can make is W = gCn =3C3 = 1.

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