# Mathematical misconception in scattering: switching from cartesian to spherical

1. Dec 22, 2012

### M. next

If we were to consider a nucleon-nucleon interaction:
We know that the incident wave (plane wave) is ψ= Ae$^{ikz}$, propagating in z direction

But for some mathematical facilities, we tend to use spherical coordinates, the wave becomes = $\frac{A}{2ik}$[e$^{ikr}$/r - e$^{-ikr}$/r]

How come?
Where did the '2ik' in the denominator come from?

2. Dec 23, 2012

### andrien

where you have seen that.
writing e(ikr) - e(-ikr)=2i sin(kr),we have second one as
sin(kr)/kr which is different from e(ikz)=e(ikr cosθ)

3. Dec 24, 2012

### M. next

What? Sorry, but I didn't get where you're pointing to.
What was written is as follows:

The incident plane wave traveling in z direction:
ψ=Ae$^{ikz}$

They then mentioned that it was mathematically easier to work with spherical waves e$^{ikr}$/r and e$^{-ikr}$/r.

Lastly, for l=0,
ψ=$\frac{A}{2ik}$( e$^{ikr}$/r - e$^{-ikr}$/r)

That was what's written in some nuclear course.

4. Dec 24, 2012

### andrien

e(ikz)lil(2l+1)jl(kr)pl(cosθ)
lil(2l+1)(i/2k)[e-i(kr-l∏/2)/r-ei(kr-l∏/2)/r] pl(cosθ)
jl(kr) is spherical bessel function and Pl you know.this form of spherical bessel can be gotten from spherical hankel functions of first and second kind(their addition).for l=o this reduces to the required form.