Quantum Tunneling for particles of equal energies but different masses

[atay5510]

Howdy,

Can anyone explain qualitatively (without using any maths) why a particle with a smaller mass has a greater probability of tunneling through a potential barrier than another particle with a larger mass but of the same total energy?

Thanks

 

[Naty1]

same reason it's easier to put a small nail in a wall rather than a big one...

if that doesn't make sense, look up scattering pehnomena...

 

[atay5510]

ummm sorry still a bit confused.

I thought maybe is had something to do with the uncertainty in positon of each particle? I read somewhere that the smaller the mass of the particle, the larger the uncertainty in position and thus a higher probability that tunneling will be successful? Not sure why a smaller mass would have a large uncertainty in position but I am still stumped

 

[PipBoy]

>>equal energies
>>different masses

consider, a larger (higher mass) particle with the same energy as a smaller particle. The Smaller particle has a great deal more uncertainty at this level, as it's wavefunction is much, much larger than the Larger particle's. Therefore, if it exists at many more places in spacetime (theoretically speaking, of course) than the other paticle, the probability for Tunnelling to occur is that much greater.

>>small nail and big nail

Couldn't put it better myself XD

 

[zonde]

It might be related to http://en.wikipedia.org/wiki/Zitterbewegung" . The bigger frequency of Zitterbewegung the smaller offset in position.

 

[atay5510]

so because the two particles have the same energies, it is obvious that the smaller particle must be moving at a higher velocity than the larger particle and thus have a greater uncertainty in position than the larger particle and therefore a greater probability of tunneling?

 

[zonde]

No, Compton wavelength that is related to this is inversely proportional to rest mass. It does not depend from momentum of particle.