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HW1Ans - Incomplete

HW1Ans - Incomplete - HaoLi Sept.2010 2 < x >= x x t dx = 2...

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Radiation Physics Homework 1 Solutions Hao Li Sept. 2010 2. 2 2 2 2 2 2 2 0 0 2 2 2 4 4 ( , ) sin ( ) [ sin( ) cos( )] 4 8 32 2 x x xL x L x L x x x t dx x dx L L L L L π π π π π < >= Ψ = = = 2 2 2 2 2 3 2 2 2 2 2 2 2 3 0 0 2 2 2 2 2 2 4 8 4 ( , ) sin ( ) [ cos( ) sin( )] 6 16 64 3 8 x x xL x x L L x x x x t dx x dx L L L L L L L π π π π π π π < >= Ψ = = = 3. If we assume the box is an infinite square well, its kinetic energy is 2 2 2 2 2 2 , , 2 2 2 8 8 8 n m l e e e h h h E n m l m L m L m L = + + When n,m,l = 1, its minimum kinetic energy is: 34 2 2 17 1,1,1 31 9 2 (6.626 10 ) 3 1 1.81 10 113 8 9.11 10 (0.1 10 ) E J J eV × = × = × = × × 4. a). 2 2 2 0 0 0 ( ) sin 1 r r d d dr π π θ ϕ θ Ψ = ∫ ∫ ∫ 2 2 2 2 0 0 0 sin 1 r N e r d d dr π π α θ ϕ θ = ∫ ∫ ∫ 2 2 2 2 0 0 0 sin 1 r N r e dr d d π π α ϕ θ θ = 2 3 4 1 4 N π α = 3 N α π = b).
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