Homework 03

# Homework 03 - EEE 434/591 Fall 2010 Homework Solutions No 3...

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EEE 434/591 Fall 2010 Homework Solutions No. 3 4. Suppose that the electrons are confined in an infinite potential well of width 0.5 nm. What spectral frequencies will result from transitions between the lowest four energy levels? Use the free electron mass The lowest energy level is given by The transitions between the lowest four levels are now given by . 5. A particle confined to an infinite potential well has an uncertainty that is of the order of the well width Δ x ~ a. The momentum can be estimated as its uncertainty value as well. Using these simple assumptions, estimate the energy of the lowest level. Compare with the actual value. If we take the uncertainty as Δ x = a , then the uncertainty in the momentum is given by Δ p = /2 Δ x = /2 a . Then, the energy can be estimated as E 1 ~ p 2 2 m ~ 1 2 m Δ p ( ) 2 ~ 1 2 m 2 a Λ Ν Μ Ξ Π Ο 2 = 2 8 ma 2 This is 4 π 2 times smaller than the actual value. 7.

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## This note was uploaded on 10/03/2010 for the course EEE 434 taught by Professor Roedel during the Fall '08 term at ASU.

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Homework 03 - EEE 434/591 Fall 2010 Homework Solutions No 3...

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