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I have tried to use nsolve to solve this transcendental equation for the bound state of a finite well..

For some reason mathematica is just returning my exact input back to me

any ideas on how to fix this?

Here is my input and output:

m = 9.11*10^-31;

b = 0.35*10^-9;

\[HBar] = 1.055*10^-34;

V = 1.602*10^-19;

and

NSolve[Sqrt[(2*m*x*b^2)/\[HBar]^2]*
   Tan[Sqrt[(2*m*x*b^2)/\[HBar]^2]] == Sqrt[(
  2*m*(V - x)*b^2)/\[HBar]^2], x]

$$ \text{NSolve}\left[\sqrt{\frac{2 b^2 m x}{\hbar ^2}} \tan \left(\sqrt{\frac{2 b^2 m x}{\hbar ^2}}\right)=\sqrt{\frac{2 b^2 m (V-x)}{\hbar ^2}},x\right] $$

with output of

NSolve[4.47806*10^9 Sqrt[x] Tan[4.47806*10^9 Sqrt[x]] == 
  4.47806*10^9 Sqrt[1.602*10^-19 - x], x]

$$ \text{NSolve}\left[4.47806\times 10^9 \sqrt{x} \tan \left(4.47806\times 10^9 \sqrt{x}\right)=4.47806\times 10^9 \sqrt{\text{1.602$\grave{ }$*${}^{\wedge}$-19}-x},x\right] $$

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  • 1
    $\begingroup$ Welcome to Mathematica.SE! I suggest the following: 0) Browse the common pitfalls question 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the faq! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! $\endgroup$ – Dr. belisarius Mar 20 '15 at 21:08
  • $\begingroup$ In addition to that, please, do not add images - add code instead. $\endgroup$ – Sektor Mar 20 '15 at 21:31
  • $\begingroup$ by images do you mean the latex version of my code as posted above? $\endgroup$ – student123 Mar 20 '15 at 21:35
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Use FindRoot:

FindRoot[Sqrt[(2*m x b^2)/h^2]*Tan[Sqrt[(2*m x b^2)/h^2]] == Sqrt[(2*m*(V - x)*b^2)/h^2], {x, 5*10^-20}]

(*Output*)
{x -> 4.86164*10^-20}
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