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**Wavefunctions for Indistinguishable and Distinguishable particles - URGENT**

## Homework Statement

A one-dimensional potential well has a set of single-particle energy eigenstates Un(x) with energies En=E_o n^2 where n=1,2,3... Two particles are placed in the well with three possible sets of properties.

a)2 distinguishable spin 0 particles

b)2 identical spin 0 particles

c)2 identical spin 1/2 particles

Write down the spatial part of the two-particle wave functions at t=0 for the two lowest energy states of the two-particle system, and hence give the degeneracies of these energy states and explain how these two-particle wavefunctions depend on time

## Homework Equations

## The Attempt at a Solution

I am getting incredibly confused by two-particle wavefunctions and between the spatial and spin states....

a) If there are 2 indenticle spin 0 particles: The wavefunction must be symmetric then would the wavefunction just be

(|0>|1> + |1>|0>)/sqrt(2)

b) 2 identicle spin 1/2 particles: The wavefunction must be antisymmetric due to Pauli Exclusion Principle so

(|0>|1> - |1> |0>)/sqrt(2)

c) 2 indistinguishable particles (boson or fermion) would it just be a wavefunction with 6 dimensions

ie phi(r1,r2)

How would you then write the spin part of the wavefunction...and how do they depend on time....

Realise this might be all wrong but I have an exam coming up and would REALLY appreciate someone clarifying this!