(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An ideal particle of energy E is incident upon a rectangular barrier of width [tex]2a[/tex] and height [tex]V_{0}[/tex]. Imagine adjusting the barrier width and height so that it approaches [tex]V(x)=\alpha \delta(x)[/tex]. What is the relationship between V_{0}, alpha and a?

2. Relevant equations

3. The attempt at a solution

I must be thinking of this incorrectly because the only thing that occurs to me is that in this limit,

[tex]V(x) = \alpha \delta (x), x = 0;

V(x) = 0, elsewhere[/tex]

and so

[tex]V_{0} = V(0) = \alpha \delta (0)[/tex]

My issue is that this doesn't include the width at all (but I'm not sure why it should since the width goes to zero). Any insights are greatly appreciated.

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# A problem with a Dirac delta function potential

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