- #1
atomicpedals
- 209
- 7
Homework Statement
Find the normalization constant N for the Gaussian wave packet
[tex]\psi (x) = N e^{-(x-x_{0})^{2}/2 K^{2}}[/tex]
Homework Equations
[tex]1 = \int |\psi (x)|^{2} dx[/tex]
The Attempt at a Solution
[tex]1 = \int |\psi (x)|^{2} dx = N^{2} \int e^{-(x-x_{0})^{2}/K^{2}} dx[/tex]
Substitute [itex]y=(x-x_{0})[/itex]
[tex]N^{2} \int e^{-y^{2}/K^{2}} dy[/tex]
Substitute again [itex]z = y/|K|[/itex]
[tex]N^{2} \int e^{-z^{2}} dz = N^{2} x_{0} K \sqrt{\pi}[/tex]
[tex]N= ( \frac{1}{K x_{0} \sqrt{\pi}})^{1/2}[/tex]
Where my question lies is with the [itex]x_{0}[/itex] in N. Should that be there?
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