Scattered State Solutions of a Repulsive Dirac Delta Potential

[PhysicsTruth]

Homework Statement

For a repulsive Dirac delta potential V = a$\delta$(x), find the scattered state solutions.

Relevant Equations

$\beta$ = $\frac{4\pi^{2}m\alpha}{h^{2}k}$
$k^{2}$ = $\frac{8\pi^{2}mE}{h^2}$

I feel that this problem can be directly answered from the E>0 case of the attractive Dirac delta potential -a$\delta$(x), with the same reflection and transmission coefficients. Can someone confirm this hunch of mine?

 

[Nate810]

Yes, your hunch is correct. The attractive Dirac delta potential -a$\delta$(x) is a special case of the more general problem of an attractive delta potential V(x). The reflection and transmission coefficients for the attractive Dirac delta potential -a$\delta$(x) are the same as those for the more general case of an attractive delta potential V(x).