Scattering amplitude of spinless particles

 In quantum mechanics, the scattering amplitude is a basic parameter that describes the interaction of particles as they scatter from one another or from a potential. The analysis is usually easier for spinless particles since the complications due to spin do not have to be considered.

Important Terms:

Scattering Amplitude:

Example: Scattering by a Spherical Potential

A spinless particle scatters off a spherical potential.  The partial wave amplitudes, can be found by solving the radial Schrödinger equation with the proper boundary conditions.    

Key Steps:

1. Solve the Radial Schrödinger Equation: Find the wavefunctions for the region inside and outside the potential.

2. Match Boundary Conditions: Ensure continuity of the wavefunctions and their derivatives at the boundary of the potential.

3. Calculate Partial Wave Amplitudes: Determine $f_{l}f\_l$ for each partial wave.

4. Sum Partial Waves: Sum the contributions from all partial waves to get the total scattering amplitude.