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Semi-Infinite Square Well Potential

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Consider the semi-infinte square well potential shown in diagram of attachment.
a. Given that the energy eigenvalue for the first excited state E2=0 (i.ie u2 is at the edge of being bound) find the width a of the well in terms of m, h and Vo. (Hint consider the continuity of u2 at x=a).
b. Calculate the energy eigenvalue E1 for the ground state u1.

See attachment for better symbol representation.

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Solution Summary

This solution uses a Matlab script and a plot to solve the transcedental equation numerically to determine the width of the well in terms of m,h and Vo as well as the calculates the energy of the eigenvalue E1 for the ground state u1. All steps are shown with brief explanations.

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The explanations are written in the attached pdf file.

I also attach the plot used to solve numerically the ...

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