Question:
Recall how in Lecture 5, we used graphical methods to obtain the energy levels of a finite potential well. Suppose we are using the same methods in the following graphs. Which graph corresponds to the deepest potential well? (Assume all the wells are of the same width.)
Solution:
We should pick the one such that the curve representing $ \sqrt{(\frac{\xi}{x})^2 - 1} $ has a largest zero crossing, that is because when the curves crosses 0, it correspond to the point when $ x = \xi $, so the curve with the largest zero crossing has the largest $ \xi $ value.
Recall how in Lecture 5, we used graphical methods to obtain the energy levels of a finite potential well. Suppose we are using the same methods in the following graphs. Which graph corresponds to the deepest potential well? (Assume all the wells are of the same width.)
Solution:
We should pick the one such that the curve representing $ \sqrt{(\frac{\xi}{x})^2 - 1} $ has a largest zero crossing, that is because when the curves crosses 0, it correspond to the point when $ x = \xi $, so the curve with the largest zero crossing has the largest $ \xi $ value.
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