- #1
Pilean
- 2
- 0
Hi!
I'm struggeling with a quantum mechanical problem.
An alpha-particle is "trapped" inside a uraniumcore, and the potential is simplified to
0 for R2 < r
V0 for R1<= r <= R2
0 for 0<= r < R1
I have calculated the transmission coefficient T = 1/(1+V02/(4E(V0-E))*sin2(sqrt(2m(V0-E)/hbar*(R1-R2)
I am now supposed to show that for k*dR >> 1, we have
T ~ K(E)*exp(-2k*dR)
Where dR = R2-R1
and k = sqrt(2m(V0-E)/hbar
And tell what K(E) is...
I have tried to use that sinx = (exp(ix)-exp(-ix))/2i, but it won't turn into the right expression..
A small additional question: For a infinate potential, is there any possibility for tunneling into this area? After what I understand from the infinite square well the probability for the particle to be in such a potential is zero?
Hope for some guidence on where to start :)
I'm struggeling with a quantum mechanical problem.
Homework Statement
An alpha-particle is "trapped" inside a uraniumcore, and the potential is simplified to
0 for R2 < r
V0 for R1<= r <= R2
0 for 0<= r < R1
I have calculated the transmission coefficient T = 1/(1+V02/(4E(V0-E))*sin2(sqrt(2m(V0-E)/hbar*(R1-R2)
I am now supposed to show that for k*dR >> 1, we have
T ~ K(E)*exp(-2k*dR)
Where dR = R2-R1
and k = sqrt(2m(V0-E)/hbar
And tell what K(E) is...
I have tried to use that sinx = (exp(ix)-exp(-ix))/2i, but it won't turn into the right expression..
A small additional question: For a infinate potential, is there any possibility for tunneling into this area? After what I understand from the infinite square well the probability for the particle to be in such a potential is zero?
Hope for some guidence on where to start :)