Calculating velocity

1. Hey,



so I have a Lorentz violating wavepacket and from this I need to find the velocity.



My wavepacket is of the form



[tex\\begin{equation}

\langle\varphi(t,x)\rangle \equiv\exp\Bigg[i\textbf{K}_M(t-x)-\frac{\Delta\textbf{K}_M}{4}(t-x)^2\Bigg]

\end{equation}[/tex]



where for this question you need to know that



[tex]K_M=k_0+\frac{t}{2M^2}K_0^3[/tex]



I did this:



[tex]

K_m(dt-dx)=k_0(dt-dx)+\frac{k_0^3}{2M^2}(t(dt-dx)+(t-x)dt)[/tex]



I only need to calculate v from the first term in the exponent and dt=dx and v=dx/dt and it must be of the form 1+...