Are Particles Theoretically Tangible?

[Jehanne]

Schrödinger's equation describes electrons, protons and many (perhaps, nearly all other, I'm not a physicist) particles.  If you want to learn more, I would suggest an undergraduate text in physics, such as Fundamentals of Physics by Halliday, Resnick and Walker.

Schrodinger's equation is a non-relativistic equation, and so does not incorporate spin or anti-matter. It is a good approximation for most atomic physics.

Dirac's equation is the relativistic version for fermions (electrons, protons) and Maxwell's equations are the version for spin 1 bosons (photons being the main example).

The philosophy slightly changes when going to field theories, with the Lagrangian being the point of focus.

Some physics professor from a University of California school did a YouTube class on QED; the first equation that he wrote on his board was,

QED = QM + SR