Prtin2D

Prtin2D - Particle in a 2-Dimensional Box g 2 h 2m 2 h 2m 2...

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Particle in a 2-Dimensional Box h 2 2m 2 x 2 Ψ + 2 y 2 Ψ + V(x,y) Ψ=ΕΨ h 2 2m 2 Ψ + V(x,y) Ψ=ΕΨ h –2 2m 2 x 2 Ψ + 2 y 2 Ψ =ΕΨ Ψ (x,y) = X (x) Y (y) for 0 x a0 y b E h 8ma 2 2 2 4 6 8 10 14 12 11 12 21 22 23 32 2 1 2 1 g 2 x 2 Ψ = Y (y) d 2 X (x) dx 2 h –2 2m Y (y) d 2 X (x) dx 2 + X (x) d 2 Y (y) dy 2 X (x) Y (y) h –2 2m 1 X (x) d 2 X (x) dx 2 + 1 Y (y) d 2 Y (y) dy 2 =Ε=? h –2 2m 1 X (x) d 2 X (x) dx 2 = E x h –2 2m 1 Y (y) d 2 Y (y) dy 2 y h –2 2m d 2 X (x) dx 2 = E x X (x) h –2 2m d 2 Y (y) dy 2 y Y (y) X (x) = 2 a 1 / 2 sin n 1 π
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