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Unformatted text preview: Energy Quantization a. λ = h/p K = p 2 /2m = h 2 /2mλ 2 b. Ground State: λ = 2L K = h 2 /8mL 2 NOT ZERO c. In general: E n = n 2 h 2 /8mL 2 d. By confining a particle, only quantized energies are allowed i. Spectra light emitted from quantized system ii. E ph = ΔE transition  iii. large λ = small E ph = small ΔE transition  Probability Density P(x) = ψx 2 Probability of finding particle between x 1 and x 2 Prob{x 1 …x 2 } = integral(P(x)) = integral(ψx 2 ) Wave Function for particle in box Ψ n (x) = sqrt(2/L)sin(nπx/L) for n th mode = Asin(nπx/L) Where A=normalization constant Energy: E n = n 2 h 2 /8mL 2 Emission Spectra: E ph = ΔE transition U x Ψ n=1 x Ψ n=2 x...
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This note was uploaded on 04/07/2008 for the course PHYS 212 taught by Professor Ladd during the Spring '08 term at Bucknell.
 Spring '08
 Ladd
 Physics

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