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I was just after an explanation of how people get to this conclusion:

Say you are looking at the Helmholtz equation in spherical co-ordinates.

You use separation of variables, you solve for the polar and azimuthal components.

Now you solve for the radial, you will find that the radial equation can be written in the form of the spherical bessel equation after a slight change of variables.

The solution to the radial part is then:

R(r) = a j_l (z) + b y_l (z)

where z(r).

I often see people do this:

Inside the sphere:

R(r) = a j_l (z)

This is fair enough, the bessel y diverges at z = 0.

However I don't understand why people say that outside the sphere:

R(r) = b y_l (z)

Why is the bessel j not involved here?

Thanks

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# Helmholtz in spherical co-ordinates - Boundary Conditions

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