Exchange operator

In quantum mechanics, the exchange operator ${\displaystyle {\hat {P}}}$, also known as permutation operator, is a quantum mechanical operator that acts on states in Fock space. The exchange operator acts by switching the labels on any two identical particles described by the joint position quantum state ${\displaystyle \left|x_{1},x_{2}\right\rangle }$. Since the particles are identical, the notion of exchange symmetry requires that the exchange operator be unitary.

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Quantum mechanics
${\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }$ Schrödinger equation
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