- #1
IHateMayonnaise
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Homework Statement
This is part of a much larger problem, however currently I am stuck at the following integral:
[tex]
\int_{-\infty}^{\infty}exp\left(k^2\left((\Delta x)^2-\frac{i \hbar t}{2m}\right ) + k(ix-2(\Delta x)^2 \bar{k}_x)\right)dk[/tex]
Where obviously everything should be taken as a constant except the plane old k's.
Homework Equations
see (1) and (3)
The Attempt at a Solution
i tried to complete the square, followed by u/du substitution which yielded one of the messiest equations I've ever seen. There is an integral I found in a table that looks promising:
[tex]\int exp(-ax^2+bx+c)dx=\sqrt{\frac{\pi}{a}} exp\left(\frac{b^2}{4a}+c\right)[/tex]
However this does not include the imaginary unit therefore I do not believe it is much use to me.
Cookies for anyone who can get me started in the right direction.
Thanks yall!
IHateMayonnaise
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