Consider the Gaussian wave packet, v(2) = A exp Poz -a %3D where po and & are real parameters. a. Show that this wave function can be normalized, dr |ú(r)² = 1, and find the corresponding amplitude A. b. Find the corresponding wave function, o(p), in the momentum repre- sentation and check its normalization. c. Calculate expectation values (r) and (p).
Consider the Gaussian wave packet, v(2) = A exp Poz -a %3D where po and & are real parameters. a. Show that this wave function can be normalized, dr |ú(r)² = 1, and find the corresponding amplitude A. b. Find the corresponding wave function, o(p), in the momentum repre- sentation and check its normalization. c. Calculate expectation values (r) and (p).
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Transcribed Image Text:Consider the Gaussian wave packet,
(x) = A exp
Por
452
where po and & are real parameters.
a. Show that this wave function can be normalized,
dr ļú(2)* = 1,
and find the corresponding amplitude A.
b. Find the corresponding wave function, o(p), in the momentum repre-
sentation and check its normalization.
c. Calculate expectation values (r) and (p).
d. Calculate the uncertainties Ar and Ap and their product.
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