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

In delta potential barrier problem Schrodinger equation we get

[tex]\psi(x)=Ae^{kx}, x<0[/tex]

[tex]\psi(x)=Ae^{-kx}, x>0[/tex]

We must get solution of

[tex]lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{-\epsilon}\frac{d^2\psi}{dx^2}dx[/tex]

2. Relevant equations

3. The attempt at a solution

[tex]lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{-\epsilon}\frac{d^2\psi}{dx^2}dx=lim_{\epsilon \rightarrow 0} \frac{d\psi}{dx}|^{\epsilon}_{-\epsilon}[/tex] and get the solution

I can say that the whole function is

[tex]\psi(x)=Ae^{-k|x|}[/tex]

I don't have first derivative in 0.

[tex]lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{-\epsilon}\frac{d^2\psi}{dx^2}dx=lim_{\epsilon \rightarrow 0} \int^{0}_{-\epsilon}\frac{d^2\psi}{dx^2}dx+lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{0}\frac{d^2\psi}{dx^2}dx=0[/tex]

Why I don't get same solution different then zero like in case

[tex]lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{-\epsilon}\frac{d^2\psi}{dx^2}dx=lim_{\epsilon \rightarrow 0} \frac{d\psi}{dx}|^{\epsilon}_{-\epsilon}[/tex]

?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Delta force

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