Open the Quantum Tunneling simulation at http://phet.colorado.edu/simulations/si
ID: 1893974 • Letter: O
Question
Open the Quantum Tunneling simulation at http://phet.colorado.edu/simulations/sims.php?sim=Quantum Tunneling and Wave Packets. This sim- ulation demonstrates behavior of the wave function of an electron. Change the potential from bar- rier/well to constant and switch from wave packet to plane wave. Click on Configure Energy and set the Average Total Energy to 1.00 eV. Keep the potential energy set to 0 eV. For parts (a) and (b) work out the answers mathematically and check them using the simulation.a. (1 points): What is the wavelength of this wave function in nm? b. (1 points): What is the period of this wave in fs (10-15) s? Note that you cannot use v = ?f
because the wave speed is not the same as the electron speed.
c. (5 points): When we first started with complex numbers we showed that complex numbers can be written as x + iy or rei?. The simulation has options to show the real part, imaginary part, magnitude, and phase.
i. In terms of x and y, what are the real part, imaginary part, magnitude, and phase of the wave function?
ii. In terms of r and ?, what are the real part, imaginary part, magnitude, and phase of the wave function?
iii. In terms of x and y what is the probability density? iv. In terms of r and ? what is the probability density?
Explanation / Answer
Open the Quantum Tunneling simulation at http://phet.colorado.edu/simulations/sims.php?sim=Quantum Tunneling and Wave Packets. This simulation demonstrates behavior of the wave function of an electron. Change the potential from barrier/well to constant and switch from wave packet to plane wave. Click on Con?gure Energy and set the Average Total Energy to 1.00 eV. Keep the potential energy set to 0 eV. For parts (a) and (b) work out the answers mathematically and check them using the simulation. a. (1 points): What is the wavelength of this wave function in nm? b. (1 points): What is the period of this wave in fs (10 -15 ) s? Note that you cannot use v = ?f because the wave speed is not the same as the electron speed. c. (5 points): When we ?rst started with complex numbers we showed that complex numbers can be written as x + iy or re i? . The simulation has options to show the real part, imaginary part, magnitude, and phase. i. In terms of x and y, what are the real part, imaginary part, magnitude, and phase of the wave function? ii. In terms of r and ?, what are the real part, imaginary part, magnitude, and phase of the wave function? iii. In terms of x and y what is the probability density? iv. In terms of r and ? what is the probability density
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