Wave-particle duality development

Erwin Schrodinger (1887-1961 Nobel Prize for physics 1932) transferred the concept of wave-particle duality of matter developed by L. V. de Broglie for electrons to the whole atom and thus developed wave mechanics. The Schrodinger equation allows a description of orbitals as the probability of the location of the electrons. Wave mechanics represented a significant development, but were subsequently shown to be insufficient. 

Einstein s idea started a truly revolutionary development in physics quantum mechanics, It opened up wide new horizons and clarified many outstanding problems in our view of the structure of matter, Quantum mechanics is based on the idea of wave-particle duality. Einstein first applied this idea to the nature of light, but it was... 

The classical theory for electronic conduction in solids was developed by Drude in 1900. This theory has since been reinterpreted to explain why all contributions to the conductivity are made by electrons which can be excited into unoccupied states (Pauli principle) and why electrons moving through a perfectly periodic lattice are not scattered (wave-particle duality in quantum mechanics). Because of the wavelike character of an electron in quantum mechanics, the electron is subject to diffraction by the periodic array, yielding diffraction maxima in certain crystalline directions and diffraction minima in other directions. Although the periodic lattice does not scattei the elections, it nevertheless modifies the mobility of the electrons. The cyclotron resonance technique is used in making detailed investigations in this field. 

A paradox which stimulated the early development of the quantum theory concerned the indeterminate nature of light. Light usually behaves as a wave phenomenon but occasionally it betrays a particle-like aspect, a schizoid tendency known as the wave-particle duality. We consider first the wave aspect of light. 

Based on these historical achievements one may ask how far one might be able to extend such quantum experiments and for what kind of objects one might still be able to show the wave-particle duality. Recently, a new set of experiments exceeding the mass and complexity of the previously used objects by about an order of magnitude has been developed in our laboratory. These far-field diffraction experiments with the fullerene molecule Ce0 will be shown in Sec. 1. 

One of the w atershed events in the development of physics and chemistry was the appearance of Einstein s landmark paper explaining the photoelectric effect, establishing the corpuscular nature of light, and leading to the modern view of the wave-particle duality of the microscopic realm. 

Thus electrons behave in some respects like particles and in other respects like waves. We are faced with the apparently contradictory wave-particle duality of matter (and of light). How can an electron be both a particle, which is a localized entity, and a wave, which is nonlocalized The qpswer is that an electron is neither a wave nor a particle, but something else. An accurate pictorial description of an electron s behavior is impossible using the wave or particle concept of classical physics. Hie concepts of classical physics have been developed from experience in the macroscopic world and do not properly describe the microscopic world. Evolution has shaped the human brain to allow it to understand and deal effectively with macroscopic phenomena. The human nervous system was not developed to deal with phenomena at the atomic and molecular level, so it is not surprising if we cannot fully understand such phenomena. 

Schrodinger developed the ideas of quantum (wave) mechanics in 1925. It was then applied to determine atomic and molecular structure. The idea of covalent bonding between two atoms based on the sharing of electron pairs was proposed by Lewis in 1916. The Lewis model (of dots and crosses to represent electrons) is still relevant and useful, but the quantum mechanical model (Chapters 2 and 12), incorporating wave-particle duality, Pauli s exclusion principle and Heisenberg s uncertainty principle, gives a deeper understanding of chemical bonds. 

Postulation and understanding of wave-particle duality was a controversial topic from the very beginning and is closely enmeshed with the origin and development of the photoelectric effect based on Einstein s hypothesis of light quanta and quantum theory. De Broglie (1924) in a seminal paper explored the reconciliation... 

Hendry, J. (1980). The development of attitudes to the wave-particle duality of light and quantum theory, 1900-1920. Annals of Science, 37, 59-79. 

An instability-induced grand transition from quantum vacuum to material existence might have created our universe. Energy and entropy gradients mediated duality developments and transitions between fermions and bosons, particles and waves, structure and phase into the process-information dualities of life patterns. At the interface to the universe, life patterns developed a preliminary finite duality between existent matter and self-consciousness fields. By this grand transition a facility of awareness beyond space and time originated that transformed its theses/antitheses tensions into creativity. 

In this section we state the postulates of quantum mechanics in terms of the properties of linear operators. By way of an introduction to quantum theory, the basic principles have already been presented in Chapters 1 and 2. The purpose of that introduction is to provide a rationale for the quantum concepts by showing how the particle-wave duality leads to the postulate of a wave function based on the properties of a wave packet. Although this approach, based in part on historical development, helps to explain why certain quantum concepts were proposed, the basic principles of quantum mechanics cannot be obtained by any process of deduction. They must be stated as postulates to be accepted because the conclusions drawn from them agree with experiment without exception. 

Having now demonstrated that a moving electron can be considered as a wave, it remained for an equation to be developed to incorporate this revolutionary idea. Such an equation was obtained and solved by Erwin Schrodinger in 1926 when he made use of the particle-wave duality ideas of de Broglie even before experimental verification had been made. We will describe this new branch of science, wave mechanics, in Chapter 2. 

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