## Rose16 one year ago 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 <<px must hold.

1. Rose16

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.

2. IrishBoy123

@Michele_Laino

3. Michele_Laino

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: $\Large \sqrt {\left\langle {{{\left( {\Delta p} \right)}^2}} \right\rangle } = \frac{\hbar }{{d\sqrt 2 }},\quad \left\langle p \right\rangle = \hbar k$

4. Rose16

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

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