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3) Evaluate the commutator, [A,B], for each of the following pairs of operators: a. Â= square; B = square root (Å\p) = \p)°, B\W) = /Tw) b. Å=x; B =4 dx c. Â=x*; B: dx d. If two operators commute, show they must share a common set of eigenfunctions. e. If two operators that represent physical observables of a system commute, what does that imply regarding the precision to which we can know these quantities?

3) Evaluate the commutator, [A,B], for each of the following pairs of operators: a. Â= square; B = square root (Å\p) = \p)°, B\W) = /Tw) b. Å=x; B =4 dx c. Â=x*; B: dx d. If two operators commute, show they must share a common set of eigenfunctions. e. If two operators that represent physical observables of a system commute, what does that imply regarding the precision to which we can know these quantities?

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3) Evaluate the commutator, [Â, B], for each of the following pairs of operators: a. Â=square ; B = square root (Â]µ) = [p}², B \µ) = /Tw) b. Â=x; B= 4 dx c. Â=x²; B: dr d. If two operators commute, show they must share a common set of eigenfunctions. e. If two operators that represent physical observables of a system commute, what does that imply regarding the precision to which we can know these quantities?
Transcribed Image Text:3) Evaluate the commutator, [Â, B], for each of the following pairs of operators: a. Â=square ; B = square root (Â]µ) = [p}², B \µ) = /Tw) b. Â=x; B= 4 dx c. Â=x²; B: dr d. If two operators commute, show they must share a common set of eigenfunctions. e. If two operators that represent physical observables of a system commute, what does that imply regarding the precision to which we can know these quantities?
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