QuestionQuestion

1. Consider the following square potential well (V0 > 0).
V(x) = -Vo, for -a ≤ x ≤ a; 0 for |x| > a

Solve the Schrödinger equation, apply the boundary condition to induce the solution to the energy eigenvalues (equation that defines the conditions of the solution).

2. Use the information from the previous question to 1) approximate the energy equation for a potential well that is deep and wide, 2) observe how the number of bound states changes in the case of a potential that is narrow and shallow. Verify the results with the simulation results.

3. Comparing the energy eigenvalues of 1) infinite potential well and 2) finite potential well of the same width, why does the finite potential well have a lower energy?

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