Physics Lecture 15

Physics Lecture 15 - Energy Quantization a. λ = h/p K = p...

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Lecture 15: What exactly is the wave? I. Waves and Probability a. Probability Density – probability per unit length b. Probability must be between 0 and 1 c. Often P(x) ~ constant Probability ~ P(x)Δx = |ψx| 2 Δx d. Probability – area under curve of graph of function Probability Density – Absolute maximum of the graph of function e. Normalization: The probability of finding the particle somewhere is 1 integral(P(x)) = integral(|ψx| 2 ) = 1 II. Particle-in-a-box a. Probability = 0 at ends since the particle cannot get out b. Ψ(x) = 0 at x = 0,L c. Node-node n=1 “ground State” n=2 “1 st excited state” n=3 “2 nd excited state” d. Ψ n (x) = Asin(nπx/L) Where A=normalization constant e. When taking integral L’s should drop out and leave you with a number III.
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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.

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