Question

Stuck on a basic improper integral

Answer 1

I have \[\Psi(x)=Ae^{-\lambda|x|}\]and I want to normalize this wave function. So I do \[\int^{\infty}_{-\infty}\Psi^{*}\Psi dx=1\]Then I get this integral \[A^2\int^{\infty}_{-\infty}e^{-2\lambda |x|}dx\]A and lambda are positive constants.

Answer 2

so I broke it down into \[A^2\int^{0}_{-\infty}e^{-2\lambda x}dx+A^2\int^{\infty}_{0}e^{-2\lambda x}dx\]

Answer 3

then I substitute \(u=-2\lambda x\), \(du=-2\lambda dx\)

Answer 4

when the limits are from -infinity to 0,
'x' is negative.
hence |x|=-x

|x|=x when x>=0
=-x when x<0

Answer 5

oh, so it should be \[A^2\int^{0}_{-\infty}e^{2\lambda x}dx+A^2\int^{\infty}_{0}e^{-2\lambda x}dx\]

Answer 6

oh man thanks very much.

Answer 7

yes.

Answer 8

welcome ^_^