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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- Spring '07
- mechanics, Hilbert space, expectation value, Department of Physics, R. D. Field