Question

1. Show that the eigenvalue problem (4.75-4.77) has no negative eigenvalues. Hint: Use an energy argument-multiply the ODE by y and integrate from r 0 to r R; use integration by parts and use the boundedness at r0 to get the boundary term to vanish. (4.75) which is Bessel's equation. Condition (4.72) leads to the boundary condition y(R)0, (4.76) and we impose the boundedness requirement y(0) bounded (4.77)

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