Electron tunneling and classic electrdynamics.

[Austin0]

Hi
Supposing that someone had come up with the hypothese of electron tunneling before the discoveries and mathematical structure of QM... Solely within the Maxwell-Lorentz mathematical structure :
1) Could it have been proven that tunneling was impossible ??

2) Could it have been predictably quantified? Probabilities of occurrence calculated for ranges of energy levels , ranges of potential barrier penetration for energy levels etc.

My knowledge of electrodynamics is totally insufficient to have any real idea so I am hoping that someone who knows both classic and QM might have some kind of answer available.
Thanks

 

[per.sundqvist]

Hi
Supposing that someone had come up with the hypothese of electron tunneling before the discoveries and mathematical structure of QM... Solely within the Maxwell-Lorentz mathematical structure :
1) Could it have been proven that tunneling was impossible ??

2) Could it have been predictably quantified? Probabilities of occurrence calculated for ranges of energy levels , ranges of potential barrier penetration for energy levels etc.

My knowledge of electrodynamics is totally insufficient to have any real idea so I am hoping that someone who knows both classic and QM might have some kind of answer available.
Thanks

Tunneling phenomena occurs in all kind of wave problems. Its a region where there is no wave propagation but a decay like solution. For example you could have overhearing between two optical fibers when distance between is around the wavelength of the light. You could see it as the "particle" photon tunnels (classically forbidden) in analogy with an electron that tunnels.

Also light and acoustic waves could be confined and quantized, its called resonance modes, where the frequency is quantized. Take that frequency and multiply with Planck's constant and you get an energy!

 

[jtbell]

Tunneling phenomena occurs in all kind of wave problems. Its a region where there is no wave propagation but a decay like solution. For example you could have overhearing between two optical fibers when distance between is around the wavelength of the light.

This is known as frustrated total internal reflection and can be observed by placing two very flat glass plates very close together without actually touching.

 

[Austin0]

This is known as frustrated total internal reflection and can be observed by placing two very flat glass plates very close together without actually touching.

Hi Although this is far from my original question it is a fascinating topic and new to me.

I am unclear on the conservation of energy regarding the evanescent wave that passes the diffraction barrier. Does this simply mean that
1) a photon that would have been reflected is now in the second medium with a loss of one photons energy from the reflected total in the first plate
or does it mean that
2) the evanescent energy that would have simply dissipated is now an active photon??

I would normally assume number 1) but with QM I am not so sure.
Also I am curious whether the evanescent wave that is presumed present even if a second plate is not, is something that is empirically detectable or is it just a theoretical assumption?
Thanks

 

[Austin0]

Tunneling phenomena occurs in all kind of wave problems. Its a region where there is no wave propagation but a decay like solution. For example you could have overhearing between two optical fibers when distance between is around the wavelength of the light. You could see it as the "particle" photon tunnels (classically forbidden) in analogy with an electron that tunnels.

Also light and acoustic waves could be confined and quantized, its called resonance modes, where the frequency is quantized. Take that frequency and multiply with Planck's constant and you get an energy!

Hi
When you say overhearing does that mean actual crossover of photons??
It would seem that statistically the exchange would be reciprocal so how do they detect the phenomenon?
When you said classically forbidden does that imply yes to 1) of my original question and no to 2) ?
Thanks for your responce you have given me some new and interesting subjects to explore.