Yukawa Potential: Analyzing Shapes & Angular Momentum

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Homework Help Overview

The discussion revolves around the Yukawa Potential, specifically analyzing the shapes of the effective potential and determining the values of angular momentum for finite or bounded motion of a particle within this potential.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to analyze the various shapes of the effective potential based on the parameters alpha and k, while expressing uncertainty regarding the angular momentum aspect. Some participants suggest graphing the potential for better understanding, while others provide insights into the relationship between angular momentum and the potential.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the potential shapes and the implications of angular momentum. Some guidance has been offered regarding the mathematical representation of angular momentum, but there is no consensus on the overall approach to the problem.

Contextual Notes

Participants are navigating the complexities of the Yukawa Potential, including the effects of varying parameters and the implications for angular momentum, which may require additional information or clarification.

the keck
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Homework Statement



A particle moves under the Yukawa Potential of (-alpha)*exp(-kr)/r where k is real. Discuss all possible shapes of the effective potential. At what values of angular momentum L can the particle move in the potential with finite/bounded motion

The Attempt at a Solution



The first part, I can sort of do, but there's so many combination of shapes, since we are saying here alpha & k could be greater or less than zero or equal to zero. The second part concerning angular momentum I am totally at a loss

Thanks

Regards,
The Keck
 
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just graph it and look! :)
 
Angular momentum gives a 1D potential L(L+1)/2mr^2.
For high enough L, the total potentiall will have no negative part.
 
I wish to have more information regarding how you come to calculate l(l+1)/2mr^2 as a angular momentum for yukawa potential
 

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