How to asign well numerical values efficiently before to plot?

Question

A problem is presented when the substitution of the numerical values for this function

Uz = (-(1/4) - I/4) (2 Sqrt[\[Pi]])/k  1/Sqrt[k R]      E^(-((2 I a n \[Pi])/\[CapitalLambda])   - (n^2 \[Pi]^2)/( b^2 \[CapitalLambda]^2) - (I (k^2 R^2 + (n \[Pi] + k z)^2))/(2  k R)) (Erfi[((1/2 + I/2) (n \[Pi] + k (-R + z)))/Sqrt[k R]] - Erfi[((1/2 + I/2) (n \[Pi] + k (R + z)))/Sqrt[k R]] + 
    Erfi[((1/2 + I/2) (k R - Sqrt[D^2 k^2 + (n \[Pi] + k z)^2]))/Sqrt[k R]] + Erfi[((1/2 + I/2) (k R + Sqrt[D^2 k^2 + (n \[Pi] + k z)^2]))/Sqrt[k R]])

I used

valplot = { k R -> 1, z -> 1,  b -> 1, z -> 0, \[CapitalLambda] -> 1 }

Ux1 = Uz /. valplot 

Please, observe that I have a variable kR and sqrt of kR. It is possible to evaluate with a unique value? It is possible to do the parameter independently. Another detail is when a product of parameters is presented. How can it is possible to fix it, this point is important for future plot analysis.

Answer 1

It would certainly be easier to specify the values of the variables independently. They appear together in the expression in several different ways.

Uz // FullForm reveals the underlying expression. Looking for the products of k and R, we find

Times[Complex[0, Rational[-1, 2]], Power[k, -1], Power[R, -1], 
 Plus[Times[Power[k, 2], Power[R, 2]]

and

Power[Times[k, R], Rational[-1, 2]]

The underlying expression of your replacement rule k R -> 1 is FullForm[k R -> 1] which gives Rule[Times[k,R],1]. This works on Power[Times[k, R], Rational[-1, 2]] because there the product between k and R is the same as on the LHS of the rule, but it doesn't work for the other ones, such as Times[Power[k, 2], Power[R, 2]], because the LHS of the rule does not match this expression.

One solution is the following:

valplot = {k R -> 1, k^-1 R^-1 -> 1, k^2 R^2 -> 1, z -> 1, b -> 1, 
   z -> 0, \[CapitalLambda] -> 1};
Ux1 = Uz //. valplot

//. must be used instead of /. because /. will only do one replacement per expression, and your expression has two products of k and R in the same which need to be replaced. //. will do that by applying the rules repeatedly until nothing changes.

You can also write the rules as

valplot = {k R -> 1, Power[k, x_] Power[R, x_] -> 1, z -> 1, b -> 1, 
   z -> 0, \[CapitalLambda] -> 1};

This will replace the both k^-1 R^-1 and k^2 R^2 using a single rule.