Question

[1 44= 9 marks ] Question 5 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?

Answer 1

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