Question

1. Consider an electron initially moving in the positive x-direction along the negative x-axis with an energy E. At the origin the potential energy U (x) changes abruptly, from U(x) = 0 for x < 0, to U(x) = 1.00 eV for x > 0. If E=1.02 eV, just higher than the barrier by 2%, what is the barrier penetration length? What is the reflectance? What is the transmittance?

2. Consider an electron initially moving in the positive x-direction along the negative x-axis with an energy of 1.0 eV. At the origin the electron encounters a square barrier; the potential energy U(x) changes abruptly, from U (x) for x < 0, to U(x) = V for 0 < x < a, and back to U(x) = 0 for x > a, where the barrier width $\alpha$ = 1.0 nm . Use the computer to make a graph of the reflectance as a function of V in electron volts. For what values of V is the electron reflected with a 5% probability?

Answer 1

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