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

Solve for u(r) in the region r>R (i.e r goes towards infinity). Show that psi(r)=(A/r)e^-alpha*r

2. Relevant equations

[tex]\frac{\(d^2u(r)}{dr^2}=\alpha^2u(r)[/tex]

[tex]\(u(r)=\psi(r)*r[/tex]

3. The attempt at a solution

[tex]\frac{\(d^2u(r)}{dr^2}=\alpha^2u(r)\Longleftrightarrow\frac{\(d^2\psi(r)*r}{dr^2}-\alpha^2\psi(r)*r=0\Longleftrightarrow\frac{\(d^2\psi(r)}{dr^2}+\frac{\(2}{r}\psi(r)-\alpha^2\psi(r)=0\Longrightarrow\mbox{characteristical equation}\Longrightarrow[/tex]

(z^2) + (2/r)z - alpha^2 = 0

which has the roots z = (-1/r) +/- ((1/r^2) + alpha^2 )^(1/2)

This doesn't seem correct. What have I done wrong? (BTW: sorry for not using LATEX everywhere; I didn't have enough time)

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# Homework Help: Differential equation, quantum physics

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