Prove that α | ϕ a ( 1 ) | ϕ b ( 2 ) 〉 + β | ϕ b ( 1 ) | ϕ a ( 2 ) 〉 cannot be written as | ψ r ( 1 ) 〉 | ψ s ( 1 ) 〉 for any one particle states | ψ r ( 1 ) 〉 and | ψ s ( 1 ) 〉 .

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Chapter 12.1, Problem 12.1P

To determine

Prove that α|ϕa(1)|ϕb(2)〉+β|ϕb(1)|ϕa(2)〉 cannot be written as |ψr(1)〉|ψs(1)〉 for any one particle states |ψr(1)〉 and |ψs(1)〉.

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