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1. (first bit) del phi = e^ikr/4*pi*r^2 * (ik - 1/r)r
7. (one person so far, quite likely wrong)
eigenvalues are 1/4 - (n^2*pi^2)/(ln2)^2 eigenfunctions are 2x^(1/2)/3(2^(3/2)-1) for n = 0 (x^(1/2)sin(n*pi*lnx/ln2))/(7/6-21/(9+4n^2*pi^2/ln2^2)) for n>0
10. a segment of a circle