Normalizing: One dimensional wave function

[Roodles01]

Homework Statement

At time t = 0 a particle is described by the 1D wave function
ψ(x,0) = (2α)^1/4 e^-ikx-α
Verify that this is normalized

Homework Equations

Er! I have just started this sort of thing, so just a bit confused.
I think I can do this if there are limits as to where the particle is restricted like the example on this wiki page, but I don't have the restrictions shown in the above question, so how do i do this?

The Attempt at a Solution

ψ(x,0) = (2α)^1/4 e^-ikx-α
To normalize we need to find the value of arbitrary constant, A, from;
∫IψI^2 dx = 1 (between ±∞)

from ψ = A(2α)^1/4 e^-ikx-α
we have
ψ^2 = A^2 (2α)^1/4 (e^-ikx-α * e^ikx-α)ψ^2 = A^2 (2α)^1/4

∫IA^2 (2α)^1/4I dx = 1 (between ±∞)

. . . . . . . . er . . . . . come to an end.
Advice or pointer if possible.
Thank you

 

[vela]

Homework Statement

At time t = 0 a particle is described by the 1D wave function
ψ(x,0) = (2α)^1/4 e^-ikx-α
Verify that this is normalized

Homework Equations

Er! I have just started this sort of thing, so just a bit confused.
I think I can do this if there are limits as to where the particle is restricted like the example on this wiki page, but I don't have the restrictions shown in the above question, so how do i do this?

The Attempt at a Solution

ψ(x,0) = (2α)^1/4 e^-ikx-α
To normalize we need to find the value of arbitrary constant, A, from;
∫IψI^2 dx = 1 (between ±∞)

from ψ = A(2α)^1/4 e^-ikx-α
we have
ψ^2 = A^2 (2α)^1/4 (e^-ikx-α * e^ikx-α)

ψ^2 = A^2 (2α)^1/4

Your mistake is in the last step: $e^{-a}e^{-a} = e^{-2a}$.