Unformatted text preview: ψ satisﬁes the anticommutation relations { ψ ( ~x ) ,ψ † ( ~ y ) } = δ ( ~x~ y ) , { ψ ( ~x ) ,ψ ( ~ y ) } = { ψ † ( ~x ) ,ψ † ( ~ y ) } = 0 . Let us specialize a twoparticle state  φ i ≡ Z d 3 ~x 1 d 3 ~x 2 φ ( t,~x 1 ,~x 2 ) ψ † ( ~x 1 ) ψ † ( ~x 2 )  i , where φ is just a function (not an operator). (a) Show that φ obeys the FermiDirac statistics, i.e., φ ( t,~x 2 ,~x 1 ) =φ ( t,~x 1 ,~x 2 ). (b) Show that φ obeys a twoparticle Schr¨odinger equation i ∂ t φ ( t,~x 1 ,~x 2 ) = ³1 2 m ∇ 2 x 11 2 m ∇ 2 x 2 + V ( ~x 1~x 2 ) ´ φ ( t,~x 1 ,~x 2 ) . To receive full credit, be sure to keep track of minus signs associated with the FermiDirac statistics in your calculations. 1...
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 Fall '10
 Okui
 Quantum Field Theory, X1, Commutator, QFT

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