- #1
scigal89
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Homework Statement
Show that the following function is not square integrable, i.e. that it is not continuous.
[tex]
\int_{-\infty}^{\infty} \left ( e^{ikx} \right )^{2}dx
[/tex]
Homework Equations
See above. Also:
[tex]
\int \left ( e^{ikx} \right )^{2}dx = -\frac{ie^{2ikx}}{2k}
[/tex]
The Attempt at a Solution
[tex]
=\lim_{A \rightarrow -\infty}\int_{A}^{C} e^{2ikx}dx+\lim_{B \rightarrow \infty}\int_{C}^{B} e^{2ikx}dx
[/tex]
How do I go from there? What would I choose for C? Can it be anything?
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