Particle in an infinite potential well

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Homework Help Overview

The problem involves a particle confined in an infinite potential well, focusing on the relationship between the uncertainty in the particle's position and the width of the well. The context is rooted in quantum mechanics and the uncertainty principle.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the uncertainty principle and how it relates to the energy levels of a particle in a potential well. There are attempts to derive the uncertainty in position based on momentum assumptions, with questions about the correctness of their expressions and the implications of sign conventions.

Discussion Status

Some participants are exploring their understanding of the uncertainty principle and its application to the problem, while others are validating their approaches and results. There is no explicit consensus, but there is acknowledgment of the correctness of certain interpretations regarding the relationship between uncertainties and the width of the well.

Contextual Notes

Participants are working under the assumption that all values are positive, which raises questions about the implications for the inequality in their results. There is also a mention of expected outcomes that may differ from participants' calculations.

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Homework Statement



The nth energy level for a particle of mass m confined in an infinite potential well is given by:

45c2b9fd81beaf323e353898e6ee4095.png


where L is the width of the well and h is Planck’s constant. Assuming that the uncertainty in the particle’s momentum is equal to the momentum itself, show that the uncertainty in the particle’s position is less than the width of the well by a factor of n.

Homework Equations



Uncertainty principle?

The Attempt at a Solution



I don't really know where to start. Help!
 
Last edited:
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I have an idea of what I'm doing now, although I've got my answer as change in x <= L/(2*pi*n) instead of L/n which seems to be what the question expects.

My method was to sub in change in P = p into the uncertainty principle, then sub that into the equation given. Then i just rearranged. What am i doing wrong?

I'm also assuming all the values are positive so the less than sign doesn't have to be flipped?
 
Last edited:
Your answer seems correct, as far as I can tell.
 
Redbelly98 said:
Your answer seems correct, as far as I can tell.

Oh ok thanks. I guess my answers still in agreement that the uncertainties less than 1/n * L.
 

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