1. Find V(x,0) for a Gaussian wave-packet (k) = Ae-a (k-ko) where A is a normalization...

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1. Find V(x,0) for a Gaussian wave-packet (k) = Ae-a² (k-ko)² where A is a normalization factor to be found. Calculate the probability of finding the particle in the region -a/2 ≤ x ≤a/2. 2. Find o(k) for a square wave-packet V(x) = Aeikoz 0 xa |x|> a Find the factor A so that (r) is normalized. Hint: Use Fourier Transform to solve above two questions. (1) 3. A 45kW broadcasting antenna emits radio waves at a frequency of 4MHz. (a) How many photons are emitted per second? (b) Is the quantum nature of the electromagnetic radiation important in analyzing the radiation emitted from this antenna? 1. Find V(x,0) for a Gaussian wave-packet (k) = Ae-a² (k-ko)² where A is a normalization factor to be found. Calculate the probability of finding the particle in the region -a/2 ≤ x ≤a/2. 2. Find o(k) for a square wave-packet V(x) = Aeikoz 0 xa |x|> a Find the factor A so that (r) is normalized. Hint: Use Fourier Transform to solve above two questions. (1) 3. A 45kW broadcasting antenna emits radio waves at a frequency of 4MHz. (a) How many photons are emitted per second? (b) Is the quantum nature of the electromagnetic radiation important in analyzing the radiation emitted from this antenna?