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Unformatted text preview: EEE 352 – Homework 4 2.26 Consider the particle in the infinite potential well as shown in Fig. 2.11. Derive and sketch the wave functions corresponding to the four lowest energy levels (use Nanohub.org to plot these functions). Using Nanohub.org, we select the standard values of all parameters except the well depth, which we set to 5 eV (in order to have more than 4 energy levels). Then, the wave functions are: 1 2 3 4 2.32 Evaluate the transmission coefficient for an electron of energy 2.2 eV impinging upon a potential barrier of 6.0 eV and thickness 1010 m. Repeat the calculation for a barrier thickness of 109 m. Assume that equation (2.62) is valid. From the notes, we have T = 1 1 + k 1 2 + γ 2 2 k 1 γ 2 sinh 2 ( γ a ) = 1 1 + V 2 4 E ( V − E ) sinh 2 ( γ a ) . We evaluate the decay constant as Hence, for 0.1 nm thickness, we have T = 1 + 6 2 4 ⋅ 2.2 ⋅ 3.8 sinh 2 ( ⋅ 9.975 × 10 9 ⋅ 10 − 10 ) − 1 = 0.404 For 1 nm thickness, this becomes...
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 Fall '09
 ALLEE
 Radioactive Decay

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