- #1
Tom_12
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Homework Statement
consider operator defined as [itex]\hat{O_A} = \hat{A} -<\hat{A}> [/itex]
show that [itex](ΔA)^2=<\hat{O_A}^2>[/itex]
Homework Equations
[itex](ΔA)^2=<\hat{A}^2>-<\hat{A}>^2[/itex]
The Attempt at a Solution
[itex](ΔA)^2=<\hat{A}^2>-<\hat{A}>^2[/itex]
[itex] = <\hat{A}^2> - (\hat{A} -\hat{O_A})^2 [/itex]
[itex] = <\hat{A}^2> - \hat{A}^2 + 2\hat{A}<\hat{O_A}> - \hat{O_A}^2 [/itex]
or
[itex]\hat{O_A} = \hat{A} -<\hat{A}>[/itex]
[itex]\hat{O_A}^2 = (\hat{A} -<\hat{A}>)^2[/itex]
[itex] \hat{O_A}^2 = \hat{A}^2-2\hat{A}<\hat{A}>+\hat{A}^2 [/itex]
But I don't know how to convert the operator [itex]\hat{O_A} [/itex] into the expectation value [itex] <\hat{O_A}> [/itex]...?