- #1
FunkyDwarf
- 489
- 0
Hi All,
I have a question regarding the WKB method for computing tunnelling through barriers.
I understand the method and the ability to arrive at a solution as given in the first part (summary) of the first page here:
http://www.physics.udel.edu/~msafrono/425/Lecture 18.pdf
Is it correct to say that the tunneling probability is given by
[tex] \left| \frac{\psi(b)}{\psi(a)}\right|^2[/tex] where a is the classical turning point and b is the end of the barrier?
If so, and one had some arbitrary potential barrier, does one not need to take into account the [tex] \frac{1}{\sqrt{p}}[/tex] factors evaluated at these end points (i.e. higher order terms in the WKB approx)? Does this give the accurate prefactor to the transmission probability T?
Cheers!
I have a question regarding the WKB method for computing tunnelling through barriers.
I understand the method and the ability to arrive at a solution as given in the first part (summary) of the first page here:
http://www.physics.udel.edu/~msafrono/425/Lecture 18.pdf
Is it correct to say that the tunneling probability is given by
[tex] \left| \frac{\psi(b)}{\psi(a)}\right|^2[/tex] where a is the classical turning point and b is the end of the barrier?
If so, and one had some arbitrary potential barrier, does one not need to take into account the [tex] \frac{1}{\sqrt{p}}[/tex] factors evaluated at these end points (i.e. higher order terms in the WKB approx)? Does this give the accurate prefactor to the transmission probability T?
Cheers!