Name: Anonymous 2009-11-16 15:43
Given the wave function:
\psi(x) = Ae^{\frac{-\left (\lambda(x-a)\right )^2}{2}}\;\;\;\;\; \lambda,a \in \mathcal{R}
So that the probability function becomes:
|\psi(x)|^2 = |A|^2e^{-\left (\lambda(x-a)\right )^2}\;\;\;\;\; \lambda,a \in \mathcal{R}
Now we state that:
\int_{-\infty}^{\infty}|\psi(x)|^2\,\mathrm{d}x = |A|^2\int_{-\infty}^{\infty}e^{-\left (\lambda(x-a)\right )^2}\,\mathrm{d}x = 1
So that:
|A|^2 = \left [\int_{-\infty}^{\infty}e^{-\left (\lambda(x-a)\right )^2}\,\mathrm{d}x\right ]^{-1}
Anyway, I can't seem to solve this last equation :/ Does anyone have any great ideas?
\psi(x) = Ae^{\frac{-\left (\lambda(x-a)\right )^2}{2}}\;\;\;\;\; \lambda,a \in \mathcal{R}
So that the probability function becomes:
|\psi(x)|^2 = |A|^2e^{-\left (\lambda(x-a)\right )^2}\;\;\;\;\; \lambda,a \in \mathcal{R}
Now we state that:
\int_{-\infty}^{\infty}|\psi(x)|^2\,\mathrm{d}x = |A|^2\int_{-\infty}^{\infty}e^{-\left (\lambda(x-a)\right )^2}\,\mathrm{d}x = 1
So that:
|A|^2 = \left [\int_{-\infty}^{\infty}e^{-\left (\lambda(x-a)\right )^2}\,\mathrm{d}x\right ]^{-1}
Anyway, I can't seem to solve this last equation :/ Does anyone have any great ideas?