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1133_Physics ProblemsTechnical Physics

# 1133_Physics ProblemsTechnical Physics - 474 P40.28...

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474 Introduction to Quantum Physics P40.28 (a) Thanks to Compton we have four equations in the unknowns φ , v , and λ : hc hc m c m c e e λ λ γ 0 2 2 = + (energy conservation) [1] h h m v e λ λ φ γ φ 0 2 = + cos cos (momentum in x direction) [2] 0 2 = h m v e λ φ γ φ sin sin (momentum in y direction) [3] ′ − = λ λ φ 0 1 2 h m c e cos b g (Compton equation). [4] Using sin sin cos 2 2 φ φ φ = in Equation [3] gives γ λ φ m v h e = 2 cos . Substituting this into Equation [2] and using cos cos 2 2 1 2 φ φ = yields h h h h λ λ φ λ φ λ φ 0 2 2 2 2 1 2 4 1 = + = cos cos cos e j e j , or ′ = λ λ φ λ 4 0 2 0 cos . [5] Substituting the last result into the Compton equation gives 4 2 1 2 1 2 1 0 2 0 2 2 2 λ φ λ φ φ cos cos cos = = h m c hc m c e e e j e j . With the substitution λ 0 0 = hc E , this reduces to cos 2 2 0 2 0 2 1 2 φ = + + = + + m c E m c E x x e e where x E m c e 0 2 . For x = = 0 700 1 37 . . MeV 0.511 MeV , this gives
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