Comment or question:
Schrodinger's wave equation is comprised of two parts, the time-dependent and time-independent components, hence your explanation collapses in on itself due to the fallacy of circular argument. There's also the fact that wavefunctions apply to all particles, not just photons, hence your photonic axiom is incorrect. Also, Heisenberg's Uncertainty Principle applies to numerous quantum state combinations, the energy and momentum relationship only being the most popularly known, hence your use of it does not include the theory in its entirety.
Answer to question:
Schrodinger's wave equation is comprised of two parts because when an atom is undergoing chemical change it can be measured as a process over a period of time. When the atom is isolated all we have is the probability of Schrodinger's wave equation that in this theory represents the probability we have with any future event at the smallest level. The wave function and the wave particle duality will apply to everything because when the atom interacts with light it forms a photon electron coupling or dipole moment. The electron represents matter therefore we have the future unfolding relative to our own energy and momentum. This future will be totally uncertain because of the probability at the heart of each atom. This can be seen mathematically in the different ways we can formulate Heisenberg's Uncertainty Principle! We have uncertainty between energy and momentum ∆×∆p×≥h/4π with the 4π representing the spherical geometry of three dimensional space. There is also uncertainty between energy and time ∆E ∆t ≥ h/2π with 2π representing cylindrical geometry that is need for the Arrow of Time or for a time line from the past into the future. This process of continuous energy exchange formed by the spontaneous absorption and emission of light can be understood totally objectively as a process of continuous creation with the future coming into existence photon by photon with each new photon electron coupling or dipole moment.
Oil painting with diagram explaining the Arrow of Time.