If you believe in an immaterial soul that interacts with our bodies, you need to believe that this equation is not right, even at everyday energies. There needs to be a new term (at minimum) on the right, representing how the soul interacts with electrons. (If that term doesn't exist, electrons will just go on their way as if there weren't any soul at all, and then what's the point?) So any respectable scientist who took this idea seriously would be asking -- what form does that interaction take? Is it local in spacetime? Does the soul respect gauge invariance and Lorentz invariance? Does the soul have a Hamiltonian? Do the interactions preserve unitarity and conservation of information?
What it means is this. If one wants to argue that our current understanding actually SUPPORTS the existence of souls and afterlife, then one MUST reformulate this equation and show exactly the physics and dynamics of such entities the way we understand all other parts of physics. Now this is very important because to CLAIM that current science are consistent with such phenomenon, or even explained it, one must provide such formalism, or else, it is just a handwaving speculation. The latter is something that Deepak Chopra has been doing, which is piggy-backing onto modern physics without providing any valid formalism for it.
But if one claims that souls and afterlife are BEYOND current-day physics, then one has to throw out everything that we know (and know to be valid since we are USING them in our everyday lives) and come up with something new. This will present a very daunting task.
We don't choose theories in a vacuum. We are allowed -- indeed, required -- to ask how claims about how the world works fit in with other things we know about how the world works. I've been talking here like a particle physicist, but there's an analogous line of reasoning that would come from evolutionary biology. Presumably amino acids and proteins don't have souls that persist after death. What about viruses or bacteria? Where upon the chain of evolution from our monocellular ancestors to today did organisms stop being described purely as atoms interacting through gravity and electromagnetism, and develop an immaterial immortal soul?
We simply can't manipulate or change one part of physics, without affecting other parts. If one proposes a new physics, then it is a valid to look at consequences of that physics and see how it affects other parts. And this is where many new theories will have problems because it has to not only predict new things, but also be consistent with others that we have verified. That's why I said it is a daunting task.