- #1
smallgirl
- 80
- 0
1. We consider the on shell wave packet:
[tex]\varphi(t,x)=\int\frac{dk}{2\pi}exp(-\frac{(k-k_{0})^{2}}{\Delta k^{2}}+ik(t-x))dk
[/tex]
I need to show it is proportional to:
[tex]exp(ik_{0}(t-x)-\frac{\triangle k^{2}}{4}(t-x)^{2})dk[/tex]
through a Fourier transform of the gaussian
3. I used a Fourier transform of the form e^(ikx) but this doesn't seem to give me the right answer as I end up with something proportional to [tex]exp(-\frac{(k-k_{0})^{2}}{\triangle k^{2}}+ikt)dk[/tex] before integrating
[tex]\varphi(t,x)=\int\frac{dk}{2\pi}exp(-\frac{(k-k_{0})^{2}}{\Delta k^{2}}+ik(t-x))dk
[/tex]
I need to show it is proportional to:
[tex]exp(ik_{0}(t-x)-\frac{\triangle k^{2}}{4}(t-x)^{2})dk[/tex]
through a Fourier transform of the gaussian
3. I used a Fourier transform of the form e^(ikx) but this doesn't seem to give me the right answer as I end up with something proportional to [tex]exp(-\frac{(k-k_{0})^{2}}{\triangle k^{2}}+ikt)dk[/tex] before integrating