Classical uncertainty principles

[danoonez]

Please check my work.

Using the first uncertainty principle:


\Delta x \Delta k \sim 1


derive the second uncertainty principle:


\Delta \omega \Delta t \sim 1



My work:


\Delta x \Delta k \sim 1



\frac {\Delta x} {\Delta t} = V \Rightarrow \Delta x = V \Delta t



V \Delta t \Delta k \sim 1



V_\textrm {group} = \frac {\Delta \omega} {\Delta k}



\frac {\Delta \omega} {\Delta k} \Delta t \Delta k \sim 1



\frac {\Delta k} {\Delta k} \Delta \omega \Delta t \sim 1



\Delta \omega \Delta t \sim 1


What do you think?

[Ed Quanta]

Looks good to me. Right on man. What were you uncertain about when you wrote this?

[danoonez]

Looks good to me. Right on man. What were you uncertain about when you wrote this?


I wasn't sure if my use of

V_\textrm {group} = \frac {\Delta \omega} {\Delta k}


was legal. But then I realized that the uncertainty principles are used for wave packets so it was fine.