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Consider the Gaussian wave packet, (x) = A exp Por (1) where Po and & are real parameters. a. Show that this wave function can be normalized, d.r v(r)* = 1, (2) %3D 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.

Consider the Gaussian wave packet, (x) = A exp Por (1) where Po and & are real parameters. a. Show that this wave function can be normalized, d.r v(r)* = 1, (2) %3D 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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Consider the Gaussian wave packet, 6(x) = A exp 1 Por (1) where Po and & are real parameters. a. Show that this wave function can be normalized, dr v(r)² = 1, (2) %3D and find the corresponding amplitude A. b. Find the corresponding wave function, (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.
Transcribed Image Text:Consider the Gaussian wave packet, 6(x) = A exp 1 Por (1) where Po and & are real parameters. a. Show that this wave function can be normalized, dr v(r)² = 1, (2) %3D and find the corresponding amplitude A. b. Find the corresponding wave function, (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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