Quantum Tunneling: Electron or Proton Has Greater Probability?

[GravityGirl]

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 probabilty 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 becuase 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 probabilty of getting through.


Any thoughts...refrences?

 

[GravityGirl]

does it have to do with that fact that a proton has a longer wavelenght than the electron at the same energy?

 

[m2003]

I would like to clarify that the concept of quantum tunneling is not limited to just electrons and protons, but can also apply to other particles such as neutrons and atoms.

To answer the question, in general, the probability of tunneling for a particle depends on its energy, the height and width of the potential barrier, and the particle's mass. In the scenario described, where the potential barrier is higher than the particle's energy, the particle would have a non-zero probability of tunneling through the barrier.

In this case, the electron and proton would have different probabilities of tunneling due to their different masses. The lighter electron would have a higher probability of tunneling compared to the proton, as its smaller mass allows it to move faster and have a larger wavefunction amplitude. This results in a higher chance for the electron to penetrate the potential barrier.

It is important to note that the probability of tunneling is not solely dependent on the particle's mass, but also on other factors such as the shape and width of the potential barrier. Therefore, it is not always the case that the electron would have a higher probability of tunneling compared to the proton.

As for references, there have been numerous studies and experiments conducted on quantum tunneling, and the results are well-documented in various scientific journals and textbooks. Some notable references include "Introduction to Quantum Mechanics" by David J. Griffiths and "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili.