Calculating Velocity: Find v from K_M Eqn

[smallgirl]

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

$$K_M=k_0+\frac{t}{2M^2}K_0^3$$

I did this:

$$K_m(dt-dx)=k_0(dt-dx)+\frac{k_0^3}{2M^2}(t(dt-dx)+(t-x)dt)$$

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+...

 

[lippyka]

v=k_0+\frac{k_0^3}{2M^2}t(dt-dx)v=k_0+\frac{k_0^3}{2M^2}t(dt-dx)=k_0+\frac{k_0^3}{2M^2}t(1+t-x)Thus, the velocity of the wavepacket is given by:v=k_0+\frac{k_0^3}{2M^2}t(1+t-x)