- #1
says
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Homework Statement
Consider the wavefunction:
Ψ(x, t) = Ae-λ|x|e−iωt
Normalise Ψ(x, t)
Homework Equations
∫ |Ψ(x, t)|2 dx = 1 (bounds from x: -∞ to +∞)
The Attempt at a Solution
Ψ(x, t) = Ae-λ|x|e−iωt
Ψ(x, t) = Ae-λ|x|−iωt
Ψ*(x, t) = Ae-λ|x|+iωt
∫ |Ψ(x, t)|2 dx = A2 ∫ e-λ|x|−iωt+(-λ|x|+iωt) dx
= A2 ∫ e-λ|x|−iωt-λ|x|+iωt dx
= A2 ∫ e-λ|x|-λ|x| dx
= A2 ∫ e-2λ|x| dx
Ok, so evaluating this integral (bounds from x: -∞ to +∞)
= A2 (-e-2λx/2λ) | x: -∞ to +∞
I tried to evaluate the integral from -∞ to 0 + 0 to +∞, but I got A2*0 = 1. I've gone through the problem a few times and I'm not really sure where I went wrong. I'm trying to do this without the help of a calculator as well. Any help would be much appreciated.