Question

Why does Gaussian packet satisfy the minimum uncertainty relation? (a) Show that the equality sign in the generalized uncertainty relation holds if the state in question satisfies A|a)=XB|) with X being purely imaginary (b) We have shown in class that the wave function for a Gaussian wave packet given by -1/4 i(px)x' (x'-(x))2 (x|a)=(2Tl2) dxe h 412 satisfies the minimum uncertainty relation (()((p.) = . Prove that the requirement (x'Ax|a) = X(x|Apx|a), with X an imaginary number is indeed satisfied for such a Gaussian wave packet, in agreement with (a) (c) Show that the expectation value of the anticommutation i and pr with respect to (a) vanishes; i.e., (a|{x,px}|a)=0.

Name: why does gaussian packet satisfy the minimum uncertainty relation a show that the equality sign in the generalized uncertainty relation holds if the state in question satisfies aaxb with x b 37832
Uploaded: 2022-01-10T04:47:15-08:00
Duration: 5 min 22 s
Channel: Ameer Said
Description: why does gaussian packet satisfy the minimum uncertainty relation a show that the equality sign in the generalized uncertainty relation holds if the state in question satisfies aaxb with x b 37832

          Why does Gaussian packet satisfy the minimum uncertainty relation?
(a) Show that the equality sign in the generalized uncertainty relation holds if the state in question satisfies
A|a)=XB|)
with X being purely imaginary (b) We have shown in class that the wave function for a Gaussian wave packet given by -1/4 i(px)x' (x'-(x))2 (x|a)=(2Tl2) dxe h 412
satisfies the minimum uncertainty relation (()((p.) = . Prove that the requirement
(x'Ax|a) = X(x|Apx|a), with X an imaginary number
is indeed satisfied for such a Gaussian wave packet, in agreement with (a) (c) Show that the expectation value of the anticommutation i and pr with respect to (a) vanishes; i.e.,
(a|{x,px}|a)=0.

why does gaussian packet satisfy the minimum uncertainty relation a show that the equality sign in the generalized uncertainty relation holds if the state in question satisfies aaxb with x b 37832

Added by Carl H.

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