Group velocity in infinite square well

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Discussion Overview

The discussion revolves around calculating the group velocity of a wave packet in an infinite square well, exploring the implications of discrete wave numbers and the nature of standing wave solutions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks guidance on calculating group velocity in the context of an infinite square well, noting their familiarity with free particles but uncertainty regarding the discrete values of k in the well.
  • Another participant provides a definition of group velocity and links to relevant Wikipedia articles, suggesting these resources may aid in understanding.
  • One participant asserts that an infinite well only allows for standing wave solutions, implying that defining group velocity in this context may not be appropriate.
  • A later reply acknowledges the standing wave nature of solutions and expresses initial skepticism about whether standing waves could support a group velocity, indicating a reconsideration of this idea.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of group velocity to standing waves in an infinite square well, with no consensus reached on whether it can be defined in this scenario.

Contextual Notes

Participants highlight the limitations of applying concepts from free particle wave packets to the discrete nature of wave functions in an infinite square well, indicating potential misunderstandings or assumptions that may need clarification.

8Apeiron8
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ello everybody,

how can I calculate the group velocity of a wave package in an infinite square well?

I know only how it can be calculated with a free particle, the derivation of the dispersion relation at the expectation value of the moment.

But in the well, there are only discrete values of k allowed.

It would help a lot if someone could send me a link or give a little help,

thanks

Apeiron
 
Physics news on Phys.org
An infinite well only allows for standing waves solutions for which it does not make sense to define group velocity.
 
Dr Du...
Standing waves!...yes, I wondered about that before I posted and figured it was
'too simple'...actually I also figured standing waves COULD support a group velocity
but having never studied that, dismissed the idea...
 
Last edited:

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