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Unformatted text preview: = <A Ψ  and (A op ↑  Ψ >) ↑ = < Ψ A op = <A ↑ Ψ  Expectation Value: The average value of the dynamical variable O is given by <O>=< Ψ O op  Ψ >=< Ψ O Ψ > and <O>=< Ψ O op  Ψ >=<O ↑ Ψ  Ψ > . Expectation Value of Hermitian Operators: The expectation values of hermitian operators are real. Proof: The expectation value of the dynamical variable H op is <H> = < Ψ H op  Ψ > and taking the complex conjugate of both sides gives <H> * = < Ψ H op  Ψ > * = < Ψ H op ↑  Ψ > = < Ψ H op  Ψ > = <H>, where I used H op = H op ↑ . Thus, <H> = <H> * , which means that <H> is real....
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.
 Spring '07
 Field
 Physics

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