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Mathematica keeps giving me the "Re" function in an evaluation, even though my parameter assumptions should be enough to deduce the real part:

Here is the latex result:

enter image description here

As you can see, I keep getting the Real function in the exponential, but I do not know how to get rid of it... My assumptions should make it clear which one is the imaginary part, since I give as assumtpions that all parameters are real...

Here is the code:

z[y_] := (B^2 + 1)^(1/4) + B/(B^2 + 1) kx;
F[n_] := Integrate[Exp[-z[y]^2]*HermiteH[n, z[y]]*Exp[-(y - y0)^2/(4 σ^2) + I k0y*y],
          {y, -Infinity, Infinity}, Assumptions -> σ > 0 && kx ∈ Reals && 
              B ∈ Reals && k0y ∈ Reals && y0 ∈ Reals];

Simplify[Abs[F[1]]^2]

16 E^(-2 Re[ Sqrt[1 + B^2] + (2 B kx)/(1 + B^2)^(3/4) + (B^2 kx^2)/(1 + B^2)^2 - Ik0y (y0 + σ^2 Ik0y)]) π Abs[(((1 + B^2)^(1/4) + B^2 (1 + B^2)^(1/4) + B kx) σ)/(1 + B^2)]^2

I guess my question is: How can I get rid of the Re function? Future computations will become much lengthier so I want to be able to short it now.

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Use Assumptions with the final Simplify.

z[y_] = (B^2 + 1)^(1/4) + B/(B^2 + 1) kx;
F[n_] = Integrate[Exp[-z[y]^2]*HermiteH[n, z[y]]* Exp[-(y - y0)^2/(4 σ^2) + I k0y*y]
                 , {y, -Infinity, Infinity}];

Simplify[Abs[F[1]]^2,
          Assumptions -> σ > 0 && kx ∈ Reals && B ∈ Reals&& k0y ∈ Reals && y0 ∈ Reals]

$16 \pi \sigma ^2 \left(\frac{B \text{kx}}{B^2+1}+\sqrt[4]{B^2+1}\right)^2 \exp \left(-2 \left(\frac{B^2 \text{kx}^2}{\left(B^2+1\right)^2}+\frac{2 B \text{kx}}{\left(B^2+1\right)^{3/4}}+\sqrt{B^2+1}+\text{k0y}^2 \sigma ^2\right)\right)$

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  • $\begingroup$ Worked like a charm, thank you. I just started using Mathematica so I falsely assumed that the assumptions given to the integral would propagate. $\endgroup$ – George Datseris Dec 14 '17 at 14:03
  • $\begingroup$ you will learn the tricks in time ;). On a quick note, if ∈ Reals fails to work, try >0. $\endgroup$ – Sumit Dec 14 '17 at 14:10
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    $\begingroup$ note you can set $Assumptions , which will get passed to anything having the Assumptions option. $\endgroup$ – george2079 Dec 14 '17 at 15:57

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