The double-slit interference of large molecule

Wu, Xiaofeng; Liu, Jiping; Ma, Ji; Zhang, Xiaoru; Liu, Han; Liu, Xiaojing; Zhang, Siqi; Li, Hong

doi:10.1007/s40509-018-0163-0

Cited by 1 publication

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“…Taking into account the variable x in Eq. ( 15) as a radius of torus x = r cos(φ), y = r sin(φ) (17) we find that Figure 1 shows a cross-section in the plane (x, z) of a toroidal bubble submerged into an irrotational flow colored here in blue. In turn, the solenoidal flow rotates around the torus axis lying in the plane (x, y) (the points about which the rotation occurs are marked by red dots).…”

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confidence: 89%

“…From the wave-particle duality principle stated by de Broglie the particle interferometry follows immediately. Now interference patterns even from heavy molecular beams such as fullerene beams [15] can easily be computed [16,17] by applying the Feynman path integral technique [18]. The principle of particle-wave duality received a more concrete and correct embodiment in Schrödinger 's "wave mechanics", which then turned into modern quantum mechanics.…”

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confidence: 99%

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Louis de Broglie Double Solution Theory Confirms the Wave-Particle Duality Principle

Sbitnev

2023

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Louis de Broglie in the beginning 20th century voices his theory of a double solution, according to which a pilot wave accompanies a particle, simulated as a point singularity, along the most optimal path from its creation on a source up to the detection. The pilot wave is a real hidden wave, which is similar to the wave function resulting from the solution of the Schrödinger equation. This theory is in agreement with de Broglie’s postulate about the matter waves. In this article we are based on the Helmholtz decomposition theorem according to which any velocity may be represented as a sum of two velocities – irrotational and solenoidal ones. The first velocity stems from the gradient of the scalar field. The second occurs from a pseudo-vector field. We proclaim that the gradients of the scalar field define guiding paths of the pilot wave. While the pseudo-vector field defines a particle solenoidal filling. We give mathematical models of the irrotational and solenoidal flows simulating the position of a particle in a guiding wave. Modified Navier-Stokes equation in pair with the continuity equation resulting in the Schrödinger equation gives such solutions consisting of superposition of the irrotational and solenoidal flow. It is declared that the guiding wave forms from the irrotational flows. In turn, the solenoidal flows underlie forming particles that travel along optimal paths slave by the guiding wave. There are described mathematical solutions of the spherical particle washed by the superfluid representing the guiding wave along which it travels.

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confidence: 89%