Answer
See the detailed answer below.
Work Step by Step
In quantum mechanics, the probability of finding a particle in a certain region is determined by the square of the wave function, \( |\psi(x)|^2 \). In this problem, we are particularly interested in the area under the \( |\psi(x)|^2 \) curve that lies outside the GaAs potential well, which corresponds to the classically forbidden region.
To estimate the probability of the electron being in the GaAlAs layers, we need to evaluate the area under the $ |\psi(x)|^2$ curve that is outside the GaAs potential well. By examining the graph of the wave function, we can make an approximate calculation.
From the mentioned graph, it appears that the area corresponding to the classically forbidden region outside the potential well is approximately 15% of the total area under the wave function curve.
Therefore, the probability that the electron will be found in one of the GaAlAs layers is about 15%.
Note that this is a rough estimate, and your estimation may vary slightly.
