Question

consider a wave packet satisfying the relation delta-x Delta-px approximately = h/2 Pi. Show that if the packet is not to spread appreciably while it passes through a fixed position, the condition Delta-px < 10 years ago

Answer 1

This is my question, I send it here because I could not write the symbols in the question place. I hope it is clear here.

Answer 2

@Michele_Laino

Answer 3

Hint:
the wave packet \( \large\left| \alpha \right\rangle \), which minimize the Heisenberg's uncertainty condition, is the gaussian wave packet , whose width is \( \large d\), for example:
\[\Large {\psi _\alpha }\left( x \right) = \frac{1}{{{\pi ^{1/4}}\sqrt d }}\exp \left( {ikx - \frac{{{x^2}}}{{2{d^2}}}} \right)\]
Using that wave packet, we can show that:
\[\Large \sqrt {\left\langle {{{\left( {\Delta p} \right)}^2}} \right\rangle } = \frac{\hbar }{{d\sqrt 2 }},\quad \left\langle p \right\rangle = \hbar k\]

Answer 4

Could you please explain in more details because I did not understand what you mean