- #1
sachi
- 75
- 1
We have a particle of energy E crossing a potential jump at x=0. for x<=0, V=0, for x>=0 V=V1
We get a wavefunction for x>=0 psi(x) = exp(-iEt/hbar)*exp(-Kx)
where K = (2m(V1-E))^0.5/hbar
N.b E<V1 so classically we get no transmission
we are asked to estimate the penetration distance, and I have found a solution which says let the penetration distance equal 1/K. I can't see physically why we would pick this (it just seems like a random number that means that the wavefunction will decrease by a factor 1/e, but I can't see why this is a sensible estimate).
Thanks
We get a wavefunction for x>=0 psi(x) = exp(-iEt/hbar)*exp(-Kx)
where K = (2m(V1-E))^0.5/hbar
N.b E<V1 so classically we get no transmission
we are asked to estimate the penetration distance, and I have found a solution which says let the penetration distance equal 1/K. I can't see physically why we would pick this (it just seems like a random number that means that the wavefunction will decrease by a factor 1/e, but I can't see why this is a sensible estimate).
Thanks