CH 39 #30 - 2 x on may be found by considering ∫ ∫ ∞...

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39.30: a) The uncertainty in the particle position is proportional to the width of ( 29 x ψ , and is inversely proportional to α . This can be seen by either plotting the function for different values of , finding the expectation value = dx x ψ x 2 2 2 for the normalized wave function or by finding the full width at half-maximum. The particle’s uncertainty in position decreases with increasing . The dependence of the expectation value
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Unformatted text preview: 2 x on may be found by considering ∫ ∫ ∞ ∞--∞ ∞--= 〉 〈 dx e dx e x x x x 2 2 2 2 2 2 = ∂ ∂-∫ ∞ ∞--dx e x 2 2 ln 2 1 , 4 1 2 1 ln 2 1 2 = ∂ ∂-= ∫ ∞ ∞--du e u where the substitution x u = has been made. (b) Since the uncertainty in position decreases, the uncertainty in momentum must increase....
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This homework help was uploaded on 04/02/2008 for the course PHYS 208 taught by Professor Ross during the Spring '08 term at Texas A&M.

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