Lect23_HeisUncPrinc - Lecture 23 Heisenberg Uncertainty...

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Lecture 23: Heisenberg Uncertainty Principle Phy851 Fall 2009
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Heisenberg Uncertainty Relation Most of us are familiar with the Heisenberg Uncertainty relation between position and momentum: How do we know this is true? Are the similar relations between other operators? 2 h Δ Δ p x
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Variance The uncertainties are also called ‘variances’ defined as Note that the variance is state-dependent What does it tell us about our state? Consider a distribution P (a) , The average of the distribution is: To estimate the width of the distribution we might consider the square of the distance from the mean: The average of this quantity is 2 2 A A a = Δ a a P a a = ) ( ( ) 2 2 ) ( a a a d = ( ) 2 2 ____ 2 2 ) ( ) ( a a a a a P a d a + = 2 2 ___ 2 2 a a a + = 2 ___ 2 ____ 2 : a a d d rms = = 2 ___ 2 a a = 2 2 A A a = Δ
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Incompatible Observables For an observable A , the only way you can have Δ a=0 is if you are in an eigenstate of A Consider two incompatible observables, A and B :
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Lect23_HeisUncPrinc - Lecture 23 Heisenberg Uncertainty...

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