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Our interpretation is based on a line of research [**1-4**] starting from the demonstration that *any kind of wave-like
features may be treated by means of an exact ray-based treatment*: a property which was thought to be reserved to the geometrical
optics approximation. *A property which, ***when applied to the currently accepted wave-mechanical equations**, directly leads to
an exact ray-based dynamical description.

It is shown in fact that, contrary to a common belief (ultimately due, as we shall see, to an excessively rigid application of the Uncertainty Principle), a classical-looking, wave-mechanical dynamics is possible, in terms of the exact trajectories of point-like particles moving, along well defined trajectories, under the*soft piloting action - free from any wave-particle energy exchange*
- of de Broglie's monochromatic matter waves.

The so-called "*Quantum Potential*" is only a particular case of a much more general *Wave Potential*, acting on any kind of waves
and determining any typically wave-like behavior.

It's therefore the simple and direct manifestation of the*pilot waves* associated by **de Broglie** to material particles.

It is shown in fact that, contrary to a common belief (ultimately due, as we shall see, to an excessively rigid application of the Uncertainty Principle), a classical-looking, wave-mechanical dynamics is possible, in terms of the exact trajectories of point-like particles moving, along well defined trajectories, under the

The so-called "

It's therefore the simple and direct manifestation of the

We synthetize our own approach [**4**] and Bohm's one in the following **Tables I** and **II**, comparing the respective (non-relativistic)
sets of equations for the motion of single particles in an external potential *V(***r**).
**TAB.I** are structurally encoded in Schrödinger's (Helmholtz-like) time-independent equation, and provide the
exact trajectories of a point-particle of assigned energy E, piloted by a monochromatic de Broglie matter wave whose objective
physical reality is undeniably certified by its observed diffractive properties.

The equations of**TAB.II**, on the other hand, provide the probability flux-lines of a wave-packet (resulting from the entire set
of stationary eigen-solutions) built up as a whole by the simultaneous solution of Schrödinger's time-dependent equation,
declaredly giving an equivalent version of the (intrinsically probabilistic) Copenhagen vision, including most "quantum
paradoxes".

The equations of

The equations of

The comparison between our merely geometrical Helmholtz coupling of monochromatic trajectories (along which point-particles
are simply driven by de Broglie's stationary waves) and the inextricably non-local coupling of any part of the physical system
involved by the "*guidance equations*" leads us to conclude that Bohmian theory is far from the spirit of our approach, aiming
to start a non-probabilistic approach (based on the currently accepted equations of Wave Mechanics) running as close as
possible to Classical Dynamics.

- A. Orefice, R. Giovanelli and D. Ditto, Found. Phys. 39, 256 (2009)
- A. Orefice, R. Giovanelli and D. Ditto, Ref.[23], Chapter 7, pg.425-453 (2012)
- A. Orefice, R. Giovanelli and D. Ditto, Annales de la Fondation Louis de Broglie, 38, 7 (2013)
- A. Orefice, R. Giovanelli and D. Ditto, (2015) arXiv:1406.4968v3 [quant-ph]
- R. E. Wyatt, pg.28 of the Conf. Proc. Quantum Trajectories, ed. by K. H. Hughes and G. Parlant, CCP6, Daresbury, (2011)
- J. Mompart, X. Oriols, Ref.[23], Introduction, pg.1-14
- M. Mattheakis, G. P. Tsironis, V. I. Kovanis, J. Opt. 14, 114006 (2012)
- A. Benseny, G. Albareda, A. S. Sanz, J. Mompart, X. Oriols, Eur. Phys. J. D, 68:286 (2014)
- W.Heisenberg, Zeitschrift für Physik, 33, 879 (1925)
- L. de Broglie, Compt. Rend. Acad. Sci. 177, pg. 517, 548, 630 (1923)
- L. de Broglie, Annales de Physique 3, 22 (1925) (Doctoral Thesis, 1924)
- C. J. Davisson, L. H. Germer, Nature 119, 558 (1927)
- E. Schrödinger, Annalen der Physik 79, pg. 361 and 489 (1926)
- E. Schrödinger, Annalen der Physik 81, 109 (1926)
- M. Born, Zeitschrift für Physik 38, 803 (1926)
- "Gaussian Beams", http://en.wikipedia.org/wiki/Gaussian_beam
- D. J. Bohm, Phys. Rev. 85, 166 (1952)
- D. J. Bohm, Phys. Rev. 85, 180 (1952)
- C. Philippidis, C. Dewdney, B. J. Hiley, Nuovo Cimento B, 52, 15 (1979)
- D. J. Bohm, B. J. Hiley, Found. Phys. 12, 1001 (1982)
- P. R. Holland, The Quantum Theory of Motion, Cambridge University Press (1992)
- D. Dürr, S. Teufel, Bohmian Mechanics, Springer -Verlag (2009)
- AA.VV., Applied Bohmian Mechanics: from Nanoscale Systems to Cosmology, ed. by X. Oriols and J. Mompart, Pan Stanford Publishing (2012)

The following papers may be download from: ArXiv.org

(Cornell University Library)

**ArXiv Publications** [link]

**arXiv:1406.4968**

*From Classical to Wave-Mechanical Dynamics*

A.Orefice, R.Giovanelli, D.Ditto

*[v3] wed, 14 Jan. ***2015**

**arXiv:1310.8077**

*Objective Reality of de Broglie's Waves*

A.Orefice, R.Giovanelli, D.Ditto

*[v7] Sat, 22 Mar ***2014**

**arXiv:1302.4247**

*Wave Mechanics without Probability*

A.Orefice, R.Giovanelli, D.Ditto

*[v7] Thu, 22 Aug ***2013**

**arXiv:1207.0130**

*The Helmholtz Wave Potential: a non-probabilistic insight into Wave Mechanics*

A.Orefice, R.Giovanelli, D.Ditto

*[v8] Tue, 16 Apr ***2013**

**arXiv:1202.6225**

*Quantum trajectories and Cushing's historical contingency*

A.Orefice, R.Giovanelli, D.Ditto

*[v2] Tue, 16 Oct ***2012**

**arXiv:1105.4973**

*Helmholtz wave trajectories in classical and quantum physics*

A.Orefice, R.Giovanelli, D.Ditto

*[v3] Sat, 29 Oct ***2011**

**arXiv:0706.3102**

*Complete Hamiltonian description of wave-like features in classical and quantum physics*

A.Orefice, R.Giovanelli, D.Ditto

*[v5] Tue, 16 Sep ***2008**

**arXiv:0705.4049**

*Beyond Geometrical Optics and Bohmian Physics: A New Exact and Deterministic Hamiltonian Approach to Wave-Like Features in Classical and Quantum Physics*

A.Orefice, R.Giovanelli, D.Ditto

*[v1] Mon, 28 May ***2007**

(Cornell University Library)

A.Orefice, R.Giovanelli, D.Ditto

A.Orefice, R.Giovanelli, D.Ditto

A.Orefice, R.Giovanelli, D.Ditto

A.Orefice, R.Giovanelli, D.Ditto

A.Orefice, R.Giovanelli, D.Ditto

A.Orefice, R.Giovanelli, D.Ditto

A.Orefice, R.Giovanelli, D.Ditto

A.Orefice, R.Giovanelli, D.Ditto

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