- #1
Vaal
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Given the state and an operator I know the uncertainty of this operator can be calculated via
(see next post latex is being weird, sorry)
(see next post latex is being weird, sorry)
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The scalar is multiplied by the identity operator. Then you can subtract them, and things work out like you'd expect.[tex]\Delta[/tex][tex]\Omega[/tex]^{2}=<[tex]\Psi[/tex]|([tex]\Omega[/tex] - <[tex]\Omega[/tex]>)^{2}|[tex]\Psi[/tex]> (hope that is legible)
but I'm confused as to how the middle, ([tex]\Omega[/tex] -<[tex]\Omega[/tex]>) is defined. Isn't this an operator minus a scalar?
I know I can also find [tex]\Delta[/tex][tex]\Omega[/tex]^{2} by summing the the products of the probabilities of all the states with the states deviation from the expected value squared, but I thought there was a way to do this with out having to know all the probabilities. Thanks.