Find the wave function of two systems of identical, noninteracting particles: first consists of two bosons
and the second of two spin-1/2 fermions.
Consider two identical, non interacting particles (1 and 2) which may exist in two different states a and b.
If the particles are indistinguishable, then we cannot tell whether the number is in state or and because both states are equally likely we write the system wave function as a linear combination of .
If the particles are bosons, the system wave function is symmetric :
If the partices are fermions, the wave function is antisymmetric
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