Transcendental-equations-for-potential-well

We solve the transcendental equations which arise in the study of potential problems.

Transcendental functions are of the type : k cot[k]= c and are have infinite zeroes.
Our example produces the following plot:

The equation is quite easy to solve, however mathematica requires us to limit the range which is done in the code.

Its a bit difficuilt to solve when both k and c are complex valued. But one can solve by equating real and complex parts.
The final solution is as below. You can use the slider to find result at any values you like.