Back in 2018 (dec 28 vixra) I put out my first attempt to make a new relativistic wave equation rooted in what I call the (kinetic) Compton momentum, rather than the standard (kinetic) momentum, that from a quantum perspective is rooted in the de Broglie wave (which is a mathematical derivative of the true matter wave the Compton wave.). My first wave equation contained i, and as I am allergic to imaginary numbers I quickly abandoned it (the day after) as I could see also one plausible solution based on total Compton momentum (instead of kinetic Compton momentum), that got rid of i in final result (canceled out). It was likely a mistake to abandon it, so now I am back to it, and this possibly is more promising than my second wave equation that I have posted here before.

Comments welcome, as paper in progress

Deeper insight on Existing and New Wave Equations in Quantum Mechanics
\(i\frac{\partial\psi}{\partial t}=\left(-ic\nabla+\frac{mc^2}{\hbar}\right)\psi\)

that also can be re-written as (because \(\bar{\lambda}=\frac{\hbar}{mc\gamma}\))

\(i\frac{\partial \psi }{\partial t} = \left( -ic\nabla +\frac{c}{\bar{\lambda}}\right)\psi\)
(please do not check against standard relativistic energy momentum relation, as that is the relativistic energy de Broglie momentum relation, and here one need the relativistic energy Compton momentum relation that is the foundation of these new wave equations. They are related, but not the same! )

relativistic, first order in time and spatial dimension, fully rooted in Compton, so valid also for v=0, not linked to a mathematical wave that converge to infinite as v approaches 0, rock solid fundament (in my 2018 version, never posted here, I also had a sign error due to error in sign of energy operator). I suspect standard QM wave equations give predictions very hard to understand as they not have dive deep enough into the rabit hole. That said I still do not understand my own equation, but then they have used decades on understanding established QM...