Bound States, Spiral Trajectories, and Redshift: A Complex-k Approach

We investigate quantum scattering processes in the complex wave number (k) plane, examining how potential-induced phase changes generate spiral trajectories through complex exponentials. By analyzing bound state energies as discrete bisections in k-space, we demonstrate these states can be mapped to specific spiral functions. We apply this framework to cosmic microwave background radiation, using its peak wavelength (0.00106 meters) to define potential well dimensions that support quantized states. The intersection of complex-k trajectories with bound state spirals suggests an interpretation of cosmological redshift as a quantum phenomenon associated with bound state energies. This approach offers a new mathematical framework for analyzing redshift mechanics in the complex-k plane.