# How do I plot a function that contains variables I have previously defined?

I am trying to plot t as a function of the variable EE which is itself included in variables I have defined. However, when I attempt to plot the function, it just returns an empty graph. Below is my code. I have also tried it without units but it makes no difference. Thanks in advance.

k = Sqrt[2*m*EE/ℏ^2];
κ = Sqrt[2*m*(-EE)/ℏ^2];
a = Quantity[8, "Angstroms"];
m = Quantity[9.11*10^-31, "Kilograms"];
ℏ = Quantity[1.055*10^-34, "Joules"*"Seconds"];
t[EE_] := Cos[k*a] + 1/2*(κ/k - k/κ)*Sin[k*a];
Plot[t[EE], {EE, 0, 20}]

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There are some small issues,

1. Your values arn't being passed through completely. This can be tested by just passing your values into the function and see if it's fully evaluated.

t[10]


$$\frac{1}{2} \left(\frac{\sqrt{\text{EE} \left(-8.1849\times 10^{37}\text{kg}\text{/(}\text{s}^2\text{J}^2)\right)}}{\sqrt{\text{EE} \left(8.1849\times 10^{37}\text{kg}\text{/(}\text{s}^2\text{J}^2)\right)}}-\frac{\sqrt{\text{EE} \left(8.1849\times 10^{37}\text{kg}\text{/(}\text{s}^2\text{J}^2)\right)}}{\sqrt{\text{EE} \left(-8.1849\times 10^{37}\text{kg}\text{/(}\text{s}^2\text{J}^2)\right)}}\right) \sin \left(\left(8 \sqrt{2}\text{\AA}\right) \sqrt{\text{EE} \left(8.1849\times 10^{37}\text{kg}\text{/(}\text{s}^2\text{J}^2)\right)}\right)+\cos \left(\left(8 \sqrt{2}\text{\AA}\right) \sqrt{\text{EE} \left(8.1849\times 10^{37}\text{kg}\text{/(}\text{s}^2\text{J}^2)\right)}\right)$$

You can see that EE is not passed as 10, this is one of the reasons your plot isn't working.

1. Plot evaluates t[x] first, before replacing EE.

2. If you use quantities, your variable must also be a quantity that fits the rest of your function. So seconds, or whatever unit it should be.

3. And the final issue, your function gives imaginary values, and this cannot be plotted via plot anyways. Unless you want just the imaginary, or real parts.

Table[t[x], {x, 1, 5, 1}]

$$\{0.0558745\, +0.998438 i,-0.551074+0.834456 i,-0.575739+0.817633 i,-0.993756+0.111574 i,0.79168\, -0.610936 i\}$$

This can be plotted if you turn k and κ into functions, and pass them directly the variables from your plot, and use only the Real or Imaginary parts.

k[ee_] := Sqrt[2*m*ee/ℏ^2];
κ[ee_] := Sqrt[2*m*(-ee)/ℏ^2];
a = 8
m = 9.11*10^-31
ℏ = 1.055*10^-34
t[EE_] := Cos[k[EE]*a] + 1/2*(κ[EE]/k[EE] - k[EE]/κ[EE])*Sin[k[EE]*a];

Plot[Re[t[x]], {x, 0, 20}, PlotRange -> All]


Though it's pretty messy.