Estimate of ground state energy for the Yukawa potential

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SUMMARY

The discussion centers on estimating the ground state energy for the Yukawa potential using the uncertainty principle. Participants reference established methods for hydrogen and harmonic oscillators but seek clarification on applying these techniques to the Yukawa potential, which includes an exponential term. The conversation highlights the need for specific references or methodologies tailored to the Yukawa potential to facilitate accurate calculations.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly the uncertainty principle.
  • Familiarity with the Yukawa potential and its mathematical representation.
  • Knowledge of ground state energy calculations for quantum systems.
  • Experience with exponential functions in physical contexts.
NEXT STEPS
  • Research the application of the uncertainty principle to the Yukawa potential specifically.
  • Study existing literature on ground state energy calculations for non-traditional potentials.
  • Explore quantum mechanics textbooks that cover advanced potential models.
  • Investigate numerical methods for estimating ground state energies in quantum systems.
USEFUL FOR

Physicists, quantum mechanics students, and researchers interested in advanced potential models and ground state energy calculations.

L_landau
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I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator, but can this be done for the Yukawa potential where you have an exponential?
 
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L_landau said:
I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator

Can you give a specific reference?
 

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