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PS1solution

# PS1solution - (a 1 60 3 250 000 000 2 60 3 500 000 000 3 60...

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(a) Λ 1 = 60 * 10^ - 10 * 2 1 3 250000000 Λ 2 = 60 * 10^ - 10 * 2 2 3 500000000 Λ 3 = 60 * 10^ - 10 * 2 3 1 250000000 Λ 4 = 60 * 10^ - 10 * 2 4 3 1000000000 Λ 5 = 60 * 10^ - 10 * 2 5 3 1250000000 Λ 6 = 60 * 10^ - 10 * 2 6 1 500000000 Λ 7 = 60 * 10^ - 10 * 2 7 3 1750000000 Λ 8 = 60 * 10^ - 10 * 2 8 3 2000000000 (b)

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E1 = 1.45 E2 = 1.55 E3 = 1.65 E4 = 1.75 E5 = 1.90 E6 = 2.10 E7 = 2.30 E8 = 2.55 1.45 1.55 1.65 1.75 1.9 2.1 2.3 2.55 k1 = 2Pi Λ 1 k2 = 2Pi Λ 2 k3 = 2Pi Λ 3 k4 = 2Pi Λ 4 k5 = 2Pi Λ 5 k6 = 2Pi Λ 6 k7 = 2Pi Λ 7 k8 = 2Pi Λ 8 500000000 Π 3 1000000000 Π 3 500000000 Π 2000000000 Π 3 2500000000 Π 3 1000000000 Π 3500000000 Π 3 4000000000 Π 3 (c) 2 PS1.nb
ListPlot @88 k1, E1 < , 8 k2, E2 < , 8 k3, E3 < , 8 k4, E4 < , 8 k5, E5 < , 8 k6, E6 < , 8 k7, E7 < , 8 k8, E8 <<D 1.0 · 10 9 1.5 · 10 9 2.0 · 10 9 2.5 · 10 9 3.0 · 10 9 3.5 · 10 9 4.0 · 10 9 1.8 2.0 2.2 2.4 data = 88 k1^2, E1 < , 8 k2^2, E2 < , 8 k3^2, E3 < , 8 k4^2, E4 < , 8 k5^2, E5 < , 8 k6^2, E6 < , 8 k7^2, E7 < , 8 k8^2, E8 << :: 250000000000000000 Π 2 9 , 1.45 > , : 1000000000000000000 Π 2 9 , 1.55 > , 9 250000000000000000 Π 2 , 1.65 = , : 4000000000000000000 Π 2 9 , 1.75 > , : 6250000000000000000 Π 2 9 , 1.9 > , 9 1000000000000000000 Π 2 , 2.1 = , : 12250000000000000000 Π 2 9 , 2.3 > , : 16000000000000000000 Π 2 9 , 2.55 >> line = Fit @ data, 8 1, q < , q D 1.47321 + 6.19422 · 10 - 20 q line . q fi k^2 1.47321 + 6.19422 · 10 - 20 k 2 (d) 2 2m eff = 6.19422 * 10^ - 20 m eff = 2 2 * 6.19422 * 10^ - 20 * 1.6 * 10^ - 19 = H 1.0546 * 10^ - 34 L ^2 2 * 6.19422 * 10^ - 20 * 1.6 * 10^ - 19 5.61098 · 10 - 31 % H 9.109 * 10^ - 31 L 0.615982 (e) Boundary is not infinite potential well, and also the model of a flat well is just a simplification (f) PS1.nb 3

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equ = Ψ '' @ xr D - k^2 * Ψ @ xr D Ψ ¢¢ @ xr D - k 2 Ψ @
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PS1solution - (a 1 60 3 250 000 000 2 60 3 500 000 000 3 60...

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