Rose16
  • Rose16
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 <
Physics
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Rose16
  • Rose16
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 <
Physics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Rose16
  • 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.
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IrishBoy123
  • IrishBoy123
Michele_Laino
  • 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: \[\Large \sqrt {\left\langle {{{\left( {\Delta p} \right)}^2}} \right\rangle } = \frac{\hbar }{{d\sqrt 2 }},\quad \left\langle p \right\rangle = \hbar k\]

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Rose16
  • Rose16
Could you please explain in more details because I did not understand what you mean

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