Exploration of similarities between classical wave mechanics and quantum mechanics

Andrei Yu. Khrennikov

The similarity between classical wave mechanics and quantum mechanics (QM) played an important role in the development of QM (starting with works of De Broglie, Schrödinger, "late Einstein", Lamb, Lande, Mandel, Marshall, Santos, Boyer, and many others). We present a new wave-type approach, so called prequantum classical statistical field theory (PCSFT). PCSFT explores an analogy between some quantum phenomena and classical theory of random fields. Quantum systems are interpreted as symbolic representations of such fields (not only for photons, cf. Lande and Lamb, but even for massive particles). All quantum averages and correlations (including composite systems in entangled states) can be represented as averages and correlations for classical random fields. In this paper PCSFT is used to provide a classical signal representation of bunching and anti-bunching. At least the latter is typically considered as essentially quantum (nonclassical) phenomenon.

Mituo Taketani, Masayuki Nagasaki

Xue You Lee

Abstract：Geometrical optics has high similarity with classical particle mechanics. After first quantization program classical particle mechanics can obtain non-relativistic quantum mechanics that suitable for micro, but quantum mechanics does not describe the photon that its static mass is zero. So whether there is a kind of "quantization " approach for geometrical optics, by which non-relativistic quantum mechanics that can be used to describe the photon can be obtained. It’s quantum mechanics of photon similar to the Schrödinger wave mechanics under the neglection of the formation and annihilation of photon. In this paper, several methods that can be used to find

Yu. P. Pyt’ev

A. Horzela

Субхон Джомирзоев

In its physical meaning, Planck’s constant turned out to be one of the corpuscular-wave quantities (CWQ) of microparticles. In turn, the newly discovered CWQ turned out to be quantities of corpuscular-wave mechanics (CWM), just as corpuscular quantities are quantities of the Newton’s corpuscular classical mechanics (CCM). At the same time, Schrödinger’s wave quantum mechanics (WQM) turned out to be in fact incomplete part of the CWM of non-relativistic electron (NE), and Newton's CCM itself turned out to be derived from the CWM macroscopic body (MB). Thus, to our great surprise, the CWM of a NE turned out to be more general form of Schrödinger’s WQM, and the CWM of a MB turned out to be more general form of Newton’s CCM. In this regard, just Abel discovered the multiplicity of algebras, and Lobachevsky discovered the multiplicity of geometries, similar to them, we encountered the multiplicity of the mechanics of physics.