IGNOU MPH 8 2026 - Define the action of the permutation operator for a system

Question

Define the action of the permutation operator $\hat{P}_{12}$ for a system of two particles 1 and 2 and two states $|\psi_P\rangle$ and $|\psi_{P'}\rangle$ . Show that $\hat{P}_{12}^2 = \hat{I}$ and determine the eigenvalues of $\hat{P}_{12}$ .

19 Jan 2026

Answer :

Word Count : 188

The permutation operator (\hat{P}*{12}) acts on a two-particle system by exchanging the states of particles 1 and 2. For two particles in states (|\psi_P\rangle) and (|\psi*{P'}\rangle), the action is defined as: [ \hat{P}*{12} \big( |\psi_P\rangle_1 \otimes |\psi*{P'}\rangle_2 \big) = |\psi_{P'}\rangle_1 \otimes |\psi_P\rangle_2 ] This means it swaps the states

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