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20085ee2_1_midterm_ee2_2008

# 20085ee2_1_midterm_ee2_2008 - Q1(a The mathematical...

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Unformatted text preview: Q1 (a) The mathematical description of electromagnetic wave composed of amplitude, wavelength and frequency in the form: t x k e A ω- ⋅ ⋅ (b) Duality between particle and wave, , p h = λ where p is the momentum and h is the plank’s constant. (c) ( ) ( ) t x p t x k e A t k p e A t ⋅- ⋅ ⋅- ⋅ ⋅ = ⇒ ⋅ = ⋅ = ω ω ω ϕ ω ϕ h h , , , (d) 2 2 2 2 2 2 2 2 h h mE k m k m p E = ⇒ = = In a cube perpendicular to (111) is k x :k y :k z =1:1:1. To solve for k, assuming k x =k y =k z =b and solving 9 2 2 2 10 95 . 2 3 2 3 3 × = = ⇒ = ⇒ = ⇒ h mE b b k b k and the wave function is just ) ( z y x b i e A + + ⋅ ⋅ (e) 7 . 4 10 13 . 2 2 2 3 ) cos( , 9 = ⇒ × = = ⋅ = = =- wavenumber b k l wavenumber x x π π α λ λ λ Q2 (a) 3 28 3 22 10 9 . 5 10 9 . 5-- × = × = m cm n ( ) eV m n h E F 54 . 5 2 8 3 3 / 2 2 / 3 3 = = π 1 2 3 4 5 6 7 8 (b) s m m E V F F / 10 39 . 1 2 6 × = = (c) ( ) 3 . 8 10 04 . 106 2 4 21 21 10 16 . 240 10 240 2 / 1 30 501 . 1 5 . 1 2 / 1 3 2 / 3 = ∂ × = ∂ ⋅ ∫ ∫-- × × E E E E h m V eV eV π . Therefore 8 states....
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20085ee2_1_midterm_ee2_2008 - Q1(a The mathematical...

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