**Quantum mechanics** is a probabilistic theory that has been developed in an abstract phase space on the scale of the atom size $\sim 10^{-10}$ m. The formalism of quantum mechanics is based on the Schrödinger and Dirac equations. Quantum mechanics can predict/calculate stable energy levels for such quantum systems, as atoms or free electrons, in the presence of applied electric and magnetic fields, etc.

In 1952 after the publication of works by David Bohm [1], which repeated de Broglie's ideas from 1927 on the particle as a pilot-wave, Louis de Broglie came back to his earlier consideration of quantum mechanics and during the next more than 30 years he worked on a double solution theory [2] for the Schrödinger equation. De Broglie strongly believed that the prevailing quantum mechanical formalism should be replaced by a more fundamental theory. In such a theory Schrödinger's wave function $\psi$ should have a strong physical meaning instead of Max Born's interpretation that the module $|\psi (\vec r)|$ prescribes a probability for the particle to occupy a position in a point $\vec r$. Many scientists including high-level scholars turned their back on Louis de Broglie, considering him crazy. Nevertheless, some eager researchers still tried to follow-up on de Broglie's and Bohm's thoughts, developing ideas that are based on so-called hidden variables. Among new interesting results, which were obtained by de Broglie in the 1960s, we can refer to works [3] where he showed that the motion of a particle should be accompanied by a variation in its mass.

Conventional quantum mechanics is not lacking conceptual difficulties; they are discussed by de Broglie [4] (see also comments by G. Lochak in the book). Some principal difficulties of quantum mechanics, such as long-range action, etc., have been discussed in papers [5,6,7].

Thus, de Broglie relationships $E = h \nu$ and $\lambda = h/p$, which allow the derivation [4] of the Schrödinger wave equation, de Broglie's concept on the motion of a particle guided by a real wave that spreads in a sub quantum medium and de Broglie's idea on a particle that moves with a variation in mass, allow us to suggest a submicroscopic mechanics for quantum particles. In addition to de Broglie's ideas, submicroscopic mechanics includes: 1) notions and peculiarities of solid state physics and 2) a rigorous mathematical background for the structure of our ordinary physical space in which all quantum mechanical phenomena occur.

**Bibliography**

[1] D. Bohm, A suggested interpretation of the quantum theory, in terms of ”hidden” variables. I. *Physical Review* **85**, 166-179; (1952). A suggested interpretation of the quantum theory, in terms of ”hidden” variables. II, *Physical Review* **85**, 180-193 (1952).

[2] L. de Broglie, Interpretation of quantum mechanics by the double solution theory, *Annales de la Fondation Louis de Broglie* **12**, no. 4, 399- 421 (1987).

[3] L. de Broglie, Sur la dynamique du corps à masse propre variable et la formule de transformation relativiste de la chaleaur, *Comptes Rendus* **264 B** (16), 1173-1175 (1967); On the basis of wave mechanics, *Comptes Rendus* **277 B**, no. 3, 71-73 (1973).

[4] L. de Broglie, *Les incertitudes d'Heisenberg et l'interpretation probabiliste de la mechanique ondulatoire* (Gauthier-Villars, Bordas, Paris, 1982), ch. 2, sect. 4. Russian translation: *Соотношения неопределенностей Гейзенберга и вероятностная интерпретация волновой механики* /Heisenberg’s uncertainty relations and the probabilistic interpretation of wave mechanics/ (Mir, Moscow, 1986), pp. 50-52.

[5] V. Krasnoholovets, On the way to submicroscopic description of nature, *Indian Journal of Theoretical Physics* **49**, no. 2, pp. 81-95 (2001) (also arXiv.org e-print archive http://arXiv.org/abs/quant-ph/9908042).

[6] V. Krasnoholovets, Can quantum mechanics be cleared from conceptual difficulties?, http://arXiv.org/abs/quant-ph/0210050.

[7] V. Krasnoholovets, On the origin of conceptual difficulties of quantum mechanics, in *Developments in Quantum Physics*, eds. F. Columbus and V. Krasnoholovets (Nova Science Publishers Inc., New York, 2004), pp. 85-109 (also http://arXiv.org/abs/physics/0412152).