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