The discussion revolves around finding the conjugate of a complex exponential function, specifically \(\varphi=exp(-x^2/x_0^2)\). Participants are exploring the implications of the variables involved, particularly whether they are real or imaginary.
The discussion is active, with participants providing insights about the conditions under which their solutions apply. There is a recognition that the nature of \(x/x_0\) affects the outcome, and some participants affirm the correctness of their reasoning based on the assumption that \(x\) and \(x_0\) are real.
Participants are considering the implications of real versus imaginary values for the variables involved, which is central to understanding the conjugate in this context.
noblegas said:Homework Statement
Find the conjugate of
[tex]\varphi[/tex]=[tex]exp(-x^2/x_0^2)[/tex]
Homework Equations
The Attempt at a Solution
Isn't the conjugate [tex]\varphi[/tex]*=[tex]exp(x^2/x_0^2)[/tex]
Dick said:Not if x and x0 are real, which I suspect they are. What is it in that case?
noblegas said:oh ,my solution would only be correct if x/x0 is imaginary.would my expression
[tex] exp(-x^2/x_0^2)[/tex] not change when taking its conjugate??
Dick said:Right, sort of. If x is imaginary the conjugate(exp(x))=exp(-x). If x is real then conjugate(exp(x))=exp(x). But your solution is only correct if (x/x0)^2 is purely imaginary.
noblegas said:but x/x0 is not purely imaginary , but completely real. So my expression would remain the same when taking its conjugate