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Homework Statement
The problem along with its solution are included as ProblemSolution.jpg.
Homework Equations
(Eq. 1) Δx ≈ λ/(sinθ)
(Eq. 2) Δp_x ≈ 2h(v/c)(sinθ) = 2(h/λ)(sinθ)
(Eq. 3) Δx Δp = ħ/2
The Attempt at a Solution
I am confused about several things. Firstly, geometrically, what is Δx and λ? I ask because I am trying to make mathematical sense of the Δx ≈ λ/(sinθ) equation rather than just memorizing it. I am not looking for any rigorous proof or anything unecessarily challenging but just an intuitive derivation.
Secondly, why does introducing the Δp_x ≈ 2h(v/c)(sinθ) = 2(h/λ)(sinθ) equation help in answering the question; that is, how does this equation “show that if we minimize Δx by reducing λ, this will result in a loss of information about the xcomponent of the electron momentum?”
Also, if the electrons and photons are in 100% horizontal (xaxis) motion, then why don't they simply slow down in the same direction or move in the opposite direction (still on the xaxis)? (The diagram implies that photons will move along the arrowlines that point toward the lens.)
I also don't understand (1.5.3). Is (1.5.3) supposed be something like (Eq. 3) from above?
I would really like to understand this problem insideout so any help in figuring this problem out will be greatly appreciated!
If more information is needed, just ask.
Thanks in advance!
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