Understanding the Uncertainty Principle and Quantum Tunneling

[r-dizzel]

uncertain about this??

evenin' all!
wonder if anyone can help...

the question is this-

(sorry by the way if this is wrong place to post this, bit of a newbee!)

an electron has 100eV of kinetic energy, its incident on a potential barrier of height 110eV. At what distance x does the probability of finding the electron fall to 1/e of its value at x = 0? compare this with what might of be expeceted from Heisenbergs uncertainty principle.

ive calculated the wavefunctions in and before the boundary but don't really understand what the questions asks "falls to 1/e of its original value"? surely e on its own is meaningless?

the final part about the Heisenbergs unc princ i get but i thought i'd complete the questions.

would really appreciate any help

over and out

r dizzel

 

[Flux = Rad]

You'll probably get a better response if you show more of your work explicitly (i.e. the wavefunctions you've calculated). Anyway, presumably you've matched the two wavefunction amplitudes such that they are continuous across the boundary? Then just find the amplitude ratio so that the new amplitude is
$$e^-^1 = \frac{1}{e^1} = \frac{1}{2.718...}$$

of the initial value.

 

[r-dizzel]

cheers dude, will have a bash