I am fairly new to mathematica so I need a little bit of help. I need to plot the zeros of an equation containing confluent hypergeometric functions. The equation i need to solve is given by the following equation:
eq[j_, δ_, ϵ_, α_, Z_] =
Exp[I*Sqrt[ϵ^2 - δ^2]]*((j - \
(Z*α*δ)/(I*Sqrt[ϵ^2 - δ^2]))*
Hypergeometric1F1[
Sqrt[j^2 - (Z*α)^2] + (Z*α*ϵ)/(I*
Sqrt[ϵ^2 - δ^2]),
1 + 2*Sqrt[j^2 - (Z*α)^2], -2*I*
Sqrt[ϵ^2 - δ^2]] + (Sqrt[
j^2 - Z^2 α^2] + (Z*α*ϵ)/(I*
Sqrt[ϵ^2 - δ^2]))*
Hypergeometric1F1[
1 + Sqrt[
j^2 - (Z*α)^2] + (Z*α*ϵ)/(I*
Sqrt[ϵ^2 - δ^2]),
1 + 2*Sqrt[j^2 - (Z*α)^2], -2*I*
Sqrt[ϵ^2 - δ^2]])
It's a rather complex function. The key is that i need to plot the zeros of this function (zeros in epsilon domain) and that for different values of delta.
So I tried this code:
Plot[(ϵ /.
Part[Solve[
eq[1/2, δ, ϵ, 0.25, 1] == 0 &&
0 < Abs@ϵ < 10, ϵ, Complexes],
3])/δ, {δ, 0, 10}]
I have to take the third piece of the list because I only need positive values op epsilon. The problem with this is that it is taking forever to run. I first tried Findroot but the fact that it needs a start value is a huge problem.