ECE 221 Fall 08 Homework # 2
September 7, 2008
2. 80 pts (a) Show that the de Broglie wavelength of a particle approaches zero faster than 1/v as its speed v approaches the speed of light. (b) Find the de Broglie wavelength of a 15 eV proton. (c) Fin
ECE 221 Fall 08 Homework #1
September 5, 2008
Due date: September 19, together with HW#2
1. 80 pts Prepare a 1-2 page QUANTITATIVE discussion of the interaction of a specific type of EM radiation with matter. Illustrate it on one example of applicat
Solution problem 2: An electron is moving freely in the x-direction. At t = 0 the electron is described by the wave function (neglect spin) y(x) = Aexp{-x2/2b2}exp{ip0x/(h/2p )}. (a) Compute the constant A such that -+ dx|y(x)|2 = 1. (b) Compute Dx a
Problem 1, solution The electron energy is E=10eV=1.610-18J. Its speed is v=(2E/m)1/2=1.88106m/s. It travels 2km in ~10-3s. The initial uncertainty in its position is Dx=10-9m. Dp=h/Dx, Dv=h/(mDx)=1.1105m/s. Dv10-3s=110m.
After 10-3s the uncertainty