Discussion Overview
The discussion revolves around the mathematical transition from Cartesian to spherical coordinates in the context of nucleon-nucleon interactions, specifically focusing on the representation of wave functions. Participants explore the implications of this transition and the appearance of specific terms in the equations.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant notes that the incident wave in Cartesian coordinates is represented as ψ= Ae^{ikz} and questions the origin of the '2ik' in the denominator when transitioning to spherical coordinates.
- Another participant points out a difference in representation, suggesting that writing e(ikr) - e(-ikr) leads to a form involving sin(kr)/kr, which they argue differs from the Cartesian representation e(ikz)=e(ikr cosθ).
- A third participant reiterates the transition from the plane wave to spherical waves, confirming the form ψ=\frac{A}{2ik}( e^{ikr}/r - e^{-ikr}/r) as noted in a nuclear course.
- A fourth participant introduces a series expansion involving spherical Bessel functions and Legendre polynomials, suggesting that this form can be derived from spherical Hankel functions, specifically for l=0.
Areas of Agreement / Disagreement
Participants express differing interpretations of the mathematical transition and the implications of specific terms, indicating that multiple competing views remain without a clear consensus.
Contextual Notes
The discussion includes assumptions about the mathematical properties of wave functions and the definitions of spherical Bessel functions and Hankel functions, which are not fully resolved.