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

write the radial equation for a particle with mass m and angular momentum l=0 which is under the influence of the following potential:

V(r)=-a*delta(r-R)

a,R>0

write all the conditions for the solution of the problem.

2. Relevant equations

Schroedinger's equation:

Hu=Eu

Hamiltonian: H=p/2m +V = pr/2m+L^2/2mr^2+V(r)

3. The attempt at a solution

since the angular momentum is zero, the radial equation appears as:

(-hbar/2m)(d^2u/dr^2)-a*delta(r-R)u=Eu

the conditions I can think of are:

1) continuity of u

2) u(infinity)= 0 (for u to be square integrable)

3) from integration of Schroedinger's equation on the interval [R-epsilon, R+epsilon] the jump in the first derivative of u at r=R should be -2mau(R)/hbar^2

but there is another condition according to the answers, that is, u(0)=0.

where does this condition come from?

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# Homework Help: QM - delta function potential

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