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;


   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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    Mar 20, 2015 at 21:31
  • $\begingroup$ by images do you mean the latex version of my code as posted above? $\endgroup$
    – student123
    Mar 20, 2015 at 21:35

1 Answer 1


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}]

{x -> 4.86164*10^-20}

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