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CRC Press eBooks

De Broglie’s Interpretation of Wave Function

Nicolae Mazilu, Maricel Agop, Ioan Mercheş

Published Sep 12, 2019• 0 citations
Publisher

Abstract

Louis de Broglie has the essential result of interpreting the physical optics based on diffraction phenomena without making any reference to the idea of harmonic oscillator and its classical dynamics in order to calculate the intensity of light. This chapter presents an equation, which shows that the density of the light particles classically conceived as material points or localized quanta, is proportional with the intensity of the classical theory of light. The effectively inadequate point of the de Broglie’s argument is in fact only the mathematical expression of his way to conclusions. de Broglie added an important attribute to the very classical notion of a light ray. However, his theory means in fact much more, far and beyond the physical theory of light. The de Broglie’s physical ray allows us to construct an interpretation based on the idea of adiabaticity.

DOI
10.1201/9780429329050-3

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Louis de Broglie has the essential result of interpreting the physical optics based on diffraction phenomena without making any reference to the idea of harmonic oscillator and its classical dynamics in order to calculate the intensity of light. This chapter presents an equation, which shows that the density of the light particles classically conceived as material points or localized quanta, is proportional with the intensity of the classical theory of light. The effectively inadequate point of the de Broglie’s argument is in fact only the mathematical expression of his way to conclusions. de Broglie added an important attribute to the very classical notion of a light ray. However, his theory means in fact much more, far and beyond the physical theory of light. The de Broglie’s physical ray allows us to construct an interpretation based on the idea of adiabaticity.
This chapter examines the wave properties of matter. Early attempts to extend the quantum ideas to the theory of matter had some limited success, but did not progress very far. Another radical idea was required before a satisfactory theory could be developed. As light has both wave and particle properties, perhaps the same is true of 'ordinary' particles such as electrons. This bold suggestion was made by Louis de Broglie in 1923, and within a few years it had been confirmed experimentally. De Broglie's wave hypothesis formed the basis for Schrödinger's equation, which was found capable of predicting the allowed energy levels in atoms and molecules, and must be regarded as one of the most important mathematical equations of modern science. Before discussing these ideas, the chapter begins by considering the classical mechanics of particles, reviewing some simple concepts that form an essential background to the quantum theory of matter.
We uphold a general viewpoint that the ideas have their own ‘objective’ dynamics, that is a dynamics independent of personalities. Every now and then, the ideas are accessible to individuals. When it comes to social expression, though, it is only a genius, among individuals, who can reach such an accessible idea as ultimate truth, even to the point where he/she succeeds to casting it into proper words, available to society at large. Beyond those words no one can ‘rationalize’, not even the genius himself. We illustrate this observation with Erwin Schrodinger’s interpretation of the wave function introduced by him to common knowledge, which has been cast into proper words by another genius, Richard Feynman, who, nevertheless, honestly acknowledged mistrusting that interpretation. In fact, Feynman always openly admitted, and effectively exercised the probabilistic interpretation of Max Born. To wit, it is guided by this kind of interpretation, that he has built the well-known version of wave mechanics, which is based entirely on the concept of probability. We argue that Feynman was actually right on both accounts – Schrodinger’s and Born’s interpretations – and show here why and how, thus revealing a few missing points in the contemporary natural philosophy. The whole argument, and the accompanying illustration, stands completely by the words of still another genius of modern physics: Louis de Broglie, whose physics is documented and developed in the present work. The construction of this physics gives us the opportunity of a historical review of significant moments of the physical knowledge
Arguments about particles or waves gave way to a recognized need for both particles and waves in the description of radiation. The confusion over particle versus wave properties was resolved by Louis de Broglie. He postulated that since light has a dual wave–particle nature, matter also has this nature. The idea was to perform a diffraction experiment with electrons. An interference pattern was demonstrated not only with electrons, but also with many kinds of material particles like protons and neutrons. However, any attempt to observe an interference pattern with neutral atoms was found difficult by the fact that atoms carried no charge as electrons do and could not penetrate through condensate matter like neutrons. The de Broglie wavelength of an electron in the smallest orbit turns out to be exactly equal to the circumference of the orbit predicted by Bohr. The interpretation of the interference phenomenon becomes more subtle when the light beams are replaced by individual photons or particles.
The objective of the work is to reveal the Association of special theory of relativity with De-Broglie wavelength of a particle. It shows that wave nature of a particle is always associated with it’s relativistic properties. The phenomena of interference, diffraction and polarization of light can only be explained on the basis of wave theory of light. These phenomena show that light possesses wave nature. However, certain phenomena like photoelectric effect, Compton effect and discrete emission and absorption of radiation can only be explained on the basis of quantum theory. According to this theory , light propagates in a small packets or quanta and behave like corpuscles or particle. This shows that light possesses particle nature. thus, we can say that light possesses dual nature. The matter also possesses the same dual nature. In order to have wave nature, the particle must satisfy the equation Where m denotes the mass of particle when it is moving with certain velocity. h=6.62×10-34 is the plank’s constant. C is the velocity of light in free space. This shows that wavelength of a material Particle depends on mass. When mathematical operation is done on above equation, it give complete quantitative properties about the wave nature of a particle.
Louis De Broglie is one of the principal architects of quantum theory. It is to him that we owe the idea of the particle as having some sort of wavelike functionality and the wave particle duality. Despite having invented this idea, de Broglie had his doubts and spent much of the rest of his life trying in vain to justify his assertion for which he had won the Nobel Prize. Essentially de Broglie’s notion of the particle as a wave is a restatement of the assumption adopted by Niels Bohr in his model for the hydrogen atom, notably that angular momentum is quantised. De Broglie does however provide us with two useful insights: that the energy levels of the atom are in some way associated with a harmonic sequence and that there is some sort of frequency multiplication process taking place within the atom.
Louis de Broglie's celebrated hypothesis transfers a problem of representation of optics to the quantum theories. Let us suppose that the fact that originated the problem in optics is the following, "The images obtained by optical instruments are limited by diffraction. Is the diffraction phenomenon exclusively restricting of the information contained in the image or does it have some physical meaning by itself?" This considered as a problem of measurement of the radiative field does not pose the question of tracing well-defined processes in the sense of the light quantum concept. Despite this the application thereto of quantum formalism makes the essentially inferring statistical nature of measurement forecasting most important. We suggest avoiding the probabilistic conception of measurement by replacing the wave-corpuscle dualistic principle with the duality one. The latter is a basic feature of projective geometry. Referring to it we shall try to include the diffraction in a geometrical model of optics and interpret in that coherent schema the point -plane "wave" dual solution. We show what experimental substantiation the proposed duality has. Lastly, we again discuss the experimental basis of wave-corpuscle dualism.