Statistical Mechanics · Problem 9.10

Statistical Mechanics of Interacting Systems: The Method of Quantized Fields — R. K. Pathria

Physics — Statistical Mechanics · symmetrized-wave-functions-bosons-fermions

Problem

Using the wave functions up(r)=1Vei(p⋅r)/ℏu_p(r) = \frac{1}{\sqrt{V}}e^{i(p\cdot r)/\hbar} to describe the motion of a free particle, write down the symmetrized wave functions for a pair of non-interacting bosons/fermions, and show that ⟨1′,2′∣U^2S/A∣1,2⟩=±⟨2′∣W^1∣1⟩⟨1′∣W^1∣2⟩.\langle 1', 2'|\hat{U}_2^{S/A}|1, 2\rangle = \pm \langle 2'|\hat{W}_1|1\rangle\langle 1'|\hat{W}_1|2\rangle.

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