Exchange operator

<p>In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, the exchange operator 
  
    
      
        
          
            
              P
              ^
            
          
        
      
    
    {\displaystyle {\hat {P}}}
  
, also known as permutation operator, is a <a href="/facts/Operator_(quantum_mechanics)/rCJw8UFz">quantum mechanical operator</a> that acts on states in <a href="/facts/Fock_space/I2PYLlhl">Fock space</a>.  The exchange operator acts by switching the labels on any two <a href="/facts/Identical_particles/qg0mHeVR">identical particles</a> described by the joint position <a href="/facts/Quantum_state/7jbxd7Dx">quantum state</a> 
  
    
      
        
          |
          
            
              x
              
                1
              
            
            ,
            
              x
              
                2
              
            
          
          ⟩
        
      
    
    {\displaystyle \left|x_{1},x_{2}\right\rangle }
  
.  Since the particles are identical, the notion of <a href="/facts/Exchange_symmetry/qg0mHeVR">exchange symmetry</a> requires that the exchange operator be <a href="/facts/Unitarity_(physics)/x2gXDAsS">unitary</a>.
</p>

Exchange operator open-in-new

Exchange operator