The basic formula of QM in its most simple form is Schrödinger's equation. That's a linear differential equation like other differential equations from classical Newtonian mechanics or Maxwell's electrodynamics.
The distinctiveness of the Schrödinger equation: The equation describes in a deterministic way the time development of a probability.
According to the Copenhagen interpretation QM is a complete theory. Hence in QM we cannot do better than deriving a probability for the outcome of our experiments. And there is no other theory which derives more precise predictions than QM - also Bohm's theory does not.
I consider a good introduction to the Copenhagen interpretation - without any mathematical formalism - the book
"Werner Heisenberg: Physics and Philosophy".
Heisenberg is one of the founders of QM.