Consider two identical particles in 1d which exist in single-particle (normalised) (x), and are in such close proximity they can be considered as indistinguishable. wave functions /a(x) and (a) write down the symmetrised two-particle wave function for the case where the particles are bosons (vb) and the case where the particles are fermions (vp). (b) show that the expectation value (xjr2)b, f is given by: (t122) в, f — (а: )a (х)ь + dx x y: (") фь( where the upper and lower signs correspond to the boson (b) and fermion (f) cases respectively, and (x")a, b denotes the expectation value of x" with respect to va, b- (c) given that the expectation value of the squared separation for the two cases is given by - m2)2). = (x2)a + (x2)b - 2(rj^2)b, f, ((x1 в. е — explain the difference in this quantity for the cases of indistinguishable bosons and fermions. what happens as the centres of each particles' wave functions are separated?
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