How to Calculate Scattering Amplitude for a Particle in a 1/r^2 Potential?

[neworder1]

Homework Statement

Use partial waves method to calculate scattering amplitude for a quantum particle scattering off the potential V(r) = a/r^2.

Homework Equations

The Attempt at a Solution

To calculate phase shifts \delta_{l} for each angular momentum's value l, it's necessary to solve Schrodnger's equation for the specified potential - but I'm unable to do it. I know that solution for a free particle can be expressed in terms of Bessel spherical functions, but in radial Schrödinger's equation we have the centrifugal term of the form l(l+1)/r^2, where l is an integer, not for arbitary potential a/r^2. Any hints?

 

[Avodyne]

The radial equation doesn't care whether or not l is an integer ...

 

[neworder1]

Ok, but in the noninteger case the solutions are special functions, from which I don\t know how to calculate the phase factors in question.

 

[Avodyne]

The asymptotic properties of Bessel functions hold whether or not the index is an integer.