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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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}]