Quantum Tunneling: Electron or Proton Has Greater Probability?

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SUMMARY

The discussion centers on the quantum tunneling probabilities of an electron and a proton approaching a potential barrier with height V greater than their shared energy E. It is established that the electron, being less massive, moves faster than the proton, resulting in a wavefunction with a larger amplitude. Consequently, the electron has a higher probability of tunneling through the barrier compared to the proton. Additionally, the relationship between particle mass and wavelength is highlighted, indicating that the proton's longer wavelength contributes to its lower tunneling probability.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of wave-particle duality
  • Knowledge of potential barriers in quantum physics
  • Familiarity with wavefunction amplitude concepts
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  • Study the implications of mass on quantum tunneling probabilities
  • Explore the concept of wavefunction amplitude in quantum mechanics
  • Investigate the relationship between particle wavelength and tunneling behavior
  • Learn about potential barriers and their effects on particle dynamics
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Students and professionals in physics, particularly those focused on quantum mechanics, as well as researchers exploring particle behavior in potential barriers.

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An electron and proton with the same energy E approch a potential barrier whose height V is greater than E. Do they have the same probability of getting through? If not, which has a greater probability? Why is that true?

So if the electron and proton have the same energy, that means that the electron must be moving faster than the proton because the proton is more massive. Becuse the electron is moving faster, would its wavefunction have a larger amplitude than that of the proton?

If that is so, then I think the electron is has a higher probability of getting through.


Any thoughts...refrences?
 
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does it have to do with that fact that a proton has a longer wavelength than the electron at the same energy?
 

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