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Insights into special cases of analytic solutions

Sketch the first three states of the potential of Figure 2 in the case where the second excited state is just barely bound in the potential.

From your sketch, determine in terms of the mass of the particle m, Planck's constant tex2html_wrap_inline574 , and the well depth tex2html_wrap_inline576 , the minimum well-width a which allows three states to be bound in the well.
Hint: This should require very little computation

Generalize your result; state the minimum well-width a required to bind 2n+1 states in the well.



Prof. Tomas Alberto Arias
Fri Apr 25 11:33:56 EDT 1997