Unformatted text preview: Name: U _____ EE138: Quiz #2 U Note: The quiz is closed book and closed note. With the exception of your calculator, the use of all electronic devices is prohibited. Please write your answers clearly. You have 15 minutes. free space potential
energy E = 2/3 Vo Vo
Region I (x<0) Region II (x>0)
x=0 Consider the step potential shown below. An electron encounters the barrier with an energy that is two‐thirds of the potential barrier. (a) What are the general solutions of the time‐independent Schrodinger equation for regions I and II? Please include expressions for the wave number in each region. (b) What two boundary conditions can be used to solve for relationships between the constants in the general solutions? (c) Qualitatively describe the probability of finding the electron in region II for the quantum mechanical and classical cases. (d) If Vo is 1 eV (1.6 x 10‐19 J), what is the wavelength of the electron in region I? (e) Qualitatively plot n versus E for an electron in a rigid well and the ‘quantum’ harmonic oscillator. Be sure to label your plots. ...
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