if I have a transcendental equation such as this one: tan(l a) = -l / sqrt (64/a^2 - l^2 ) Where
l=sqrt(2m(E+V) /hbar^2 ) and 'a' is the width of a finite square well, how can I solve this equation in terms of both l and a. I have successfully graphed the two sides of the equation together by assuming 'a' to be any constant, i.e 1 . but how can I graphically solve it and extract an exact solution for E that includes a.
note: there are supposed to be three bound states:3 different solutions for E
l=sqrt(2m(E+V) /hbar^2 ) and 'a' is the width of a finite square well, how can I solve this equation in terms of both l and a. I have successfully graphed the two sides of the equation together by assuming 'a' to be any constant, i.e 1 . but how can I graphically solve it and extract an exact solution for E that includes a.
note: there are supposed to be three bound states:3 different solutions for E
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