We will analyze here the development of Theoretical Physics after the establishment of laws of Classical Mechanics by Newton.

Nlewton saw the macroscopic bodies to move through rectilinear trajectories (when it is null the resultant of forces on a body), and that's why he supposed that the rectilinear trajectory is universal for any body in which it is null the resultant of forces applied on it.

But in the microscopic world the elementary particles move through the helical trajectory (zitterbewegung) when it is null the resultant of forces applied on the particle, as Dirac has demonstrated (without to know it) when he developed his equation of the electron.

Well, but the whole mathematical structure of Physics has been developed on the Newtonian theory which considers the rectilinear trajectory. Fundamental concepts, like kinetic energy, were established after Newton by supposing that all the bodies move (in the absence of force) through the rectilinear trajectory.

The mathematical structure has been all developed from there. The Laplacian, the Hamiltonian, the Lagrangean, and (if we can call them so) the Maxwellian, the Einstenian, until to arrive to the Bohrian. That mathematical structure was an heritage from Newton's concept of rectilinear trajectory.

When the theorists started to develop the quantum theory, they noted that those apparatuses inherited from Newton's theory was insatisfactory for the mathematical description of the atomic world (which is not a surprise, since the Newtonian trajectory was rectilinear, but the elementary particles move through the helical trajectory, and therefore the mathematical apparatus inherited from Newton could not be able to describe the behavior of atomic particles)

Then what did happen?

Just did happen a degeneration. It was impossible to conciliate physical models with the mathematics (which is not surprise, because starting from the rectilinear trajectory we cannot describe the behavior of particles that move through the helical trajectory).

And so the solutions came in this way: the suppression of the concept of trajectory, the Physics became purely mathematical (without connection with the physical reality), and the theorists started to try to explain the fundamental structure of matter (and its laws) through pure mathematical concepts, as symmetries, topology, etc, because the Newtonian laws could not be conciliated with the mathematics required by the atom's behavior.

If the Nature really works through the helical trajectory, as proposed in the QUANTUM RING THEORY, then shall be necessary to develop all the mathematical apparatus again, that is, to make the same that was made after Newton (by Laplace, Lagrange, Hamilton, and others) but now considering the helical trajectory.

What the success of Quantum Mechanics has shown is actually the following: by considering suitable simplifications, it is possible to describe the behavior of the helical trajectory through the mathematical formalism of Quantum Mechanics.
For example, Schroedinger has started to develop his equation from the following equation of a wave:

Q(x.t) = cos(kx – wt) + Ysin(kx – wt)…………….eq. (1)

Well, but such equation represents an approach to the behavior of the helical trajectory. If we introduce some mathematical tools, eq. (1) is able to describe the behavior of the helical trajectory. These mathematical tools are just the operators (alpha, beta, gamma) determined along the development of Schroedinger's equation.

Schroedinger developed his equation taking as a point of departure the de Brolgie's relation for the duality wave-particle:
& =h/p ………….. eq. (2)
where "&" is the wavelength

In Quantum Mechanics the duality wave-particle is considered a property of the matter

But in the QUANTUM RING THEORY the relation & =h/p is considered a property of the helical trajectory
That's why, if we start to develop a formalism by using together the eq. (1) and the eq. (2), as did Schroedinger, we have to introduce some corrections, because eq. (2) is a property of the helical trajectory, but eq. (1) is not the exact picture of the helical trajectory.

In the QUANTUM RING THEORY it is shown that from the adoption of the helical trajectory we start to understand why the operator P appears in the mathematical formalism of Quantum Mechanics. So, we start to understand why to every observable p there corresponds just that sort of operator P defined in Quantum Mechanics

Reading the QUANTUM RING THEORY, the reader finaly understands that Schroedinger Equation is actually the equation of the helical trajectory.

So, without to know, what Schroedinger discovered is actually the equation of the helical trajectory, as it is shown in QUANTUM RING THEORY.

From such conclusion the reader starts to understand the successes of Quantum Mechanics.