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Show that in a parabolic potential well, the spacing between the energy levels is constant. In...

Show that in a parabolic potential well, the spacing between the energy levels is constant. In semiconductors, parabolic potential wells are often produced by using narrow square potential wells where the well to barrier width ratio gradually changes. Use the virtual crystal approximation to design a GaAs/AlAs parabolicwell where the level spacing for the electron is approximately 8meV. (Hint: This isthe harmonic oscillatorproblem.)

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