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(a) Use the properties of the Gaussian probability distribution to confirm that the expectation values of the position and the square of the position are (x) = 0 and (x) = (b) Show, without lengthy calculation, that the expectation values of the momentum and the square of the momentum are () =0 and ()- (Hint: I suggest you use your skill at integration by parts to show that d'y AP AP dr, xp xp 卫里「- and also make use of the integrals used in part (a).] (e) Hence show that the uncertainty in position, Ax, and the uncertainty in momentum, Ap, for this particle obey the relation Ar Ap=

(a) Use the properties of the Gaussian probability distribution to confirm that the expectation values of the position and the square of the position are (x) = 0 and (x) = (b) Show, without lengthy calculation, that the expectation values of the momentum and the square of the momentum are () =0 and ()- (Hint: I suggest you use your skill at integration by parts to show that d'y AP AP dr, xp xp 卫里「- and also make use of the integrals used in part (a).] (e) Hence show that the uncertainty in position, Ax, and the uncertainty in momentum, Ap, for this particle obey the relation Ar Ap=

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(a) Use the properties of the Gaussian probability distribution to confirm that the expectation values of the position and the square of the position are (x) = 0 and (x) = (b) Show, without lengthy calculation, that the expectation values of the momentum and the square of the momentum are () =0 and ()- (Hint: I suggest you use your skill at integration by parts to show that d'y AP AP dr, xp xp 卫里「- and also make use of the integrals used in part (a).] (e) Hence show that the uncertainty in position, Ax, and the uncertainty in momentum, Ap, for this particle obey the relation Ar Ap=
Transcribed Image Text:(a) Use the properties of the Gaussian probability distribution to confirm that the expectation values of the position and the square of the position are (x) = 0 and (x) = (b) Show, without lengthy calculation, that the expectation values of the momentum and the square of the momentum are () =0 and ()- (Hint: I suggest you use your skill at integration by parts to show that d'y AP AP dr, xp xp 卫里「- and also make use of the integrals used in part (a).] (e) Hence show that the uncertainty in position, Ax, and the uncertainty in momentum, Ap, for this particle obey the relation Ar Ap=
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