Quantum theory wave-particle duality

Electromagnetic waves have all the properties of waves in general reflection, refraction, interference, diffraction. However, through the magic of quantum theory ( wave-particle duality ), they may also behave like quantized particles or photons . The energy ( ) of any photon is related to its frequency ... 

If they were to account for the spectrum of atomic hydrogen and then atoms of the other elements, scientists of the early twentieth century had to revise the nineteenth-century description of matter to take into account wave-particle duality. One of the first people to formulate a successful theory (in 1927) was the Austrian scientist Erwin Schrodinger (Fig. 1.23), who introduced a central concept of quantum theory. 

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 basic understanding of the quantum theory is essential in many areas of chemistry, especially in connection with spectroscopy and with theories of atomic and molecular structure. The present book gives an introduction to the theory, and its application to elementary atomic structure, but chemical bonding is not discussed. I have tried to put the essential ideas in their historical context, but without retaining the historical introduction which has been traditional with this topic. With the crucial and difficult concepts of wave-particle duality, it seemed to me more important to give modem illustrations to show that they have current applications in chemistry. 

The first inference of photon mass was made by Einstein and de Broglie on the assumption that the photon is a particle, and behaves as a particle in, for example, the Compton and photoelectric effects. The wave-particle duality of de Broglie is essentially an extension of the photon, as the quantum of energy, to the photon, as a particle with quantized momentum. The Beth experiment in 1936 showed that the photon has angular momentum, whose quantum is h. Other fundamental quanta of the photon are inferred in Ref. 42. In 1930, Proca [43] extended the Maxwell-Heaviside theory using the de Broglie guidance theorem ... 

Planck, M. 1858-1947 Quantum theory of light and radiation wave/particle duality Mason (1961)... 

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. 

Wave-particle duality accounts for the probabilistic nature of quantum mechanics and for indeterminacy. Once we accept that particles can behave as waves, then we can apply the resnlts of classical electromagnetic theory to particles. By analogy, the probability is the sqnare of the amplitnde. Zero-point energy is a con-seqnence of the Heisenberg nncertainty relation all particles bound in potential wells have finite energy even at the absolnte zero of temperature. 

Quantum chemistry is the appfication of quantum mechanical principles and equations to the study of molecules. In order to nnderstand matter at its most fundamental level, we must use quantum mechanical models and methods. There are two aspects of quantum mechanics that make it different from previous models of matter. The first is the concept of wave-particle duality that is, the notion that we need to think of very small objects (such as electrons) as having characteristics of both particles and waves. Second, quantum mechanical models correctly predict that the energy of atoms and molecules is always quantized, meaning that they may have only specific amounts of energy. Quantum chemical theories allow us to explain the structure of the periodic table, and quantum chemical calculations allow us to accurately predict the structures of molecules and the spectroscopic behavior of atoms and molecules. 

The wave theory of light reached its climax with Hertz s contributions around 1888. Physics was now in a state of turmoil, tom apart by the wave-particle duality caused by the quantum theory. As a result, research in photo- and opto-related areas was divided into two streams quantum electrodynamics and molecular spectroscopy. 

The answers to the above questions, not all of which need he presented here, were formulated between 1925 and 1926, in the revolution of modern quantum theory, which shook the foundations of physics and philosophy. Remarkably, the central theme of quantum theory was the nature of light, and what came to be called the wave-particle duality. But other broader implications of the new theory existed, and the first inkling of this was given in 1924 by Louis de Broglie (Fig. 3.26) in his doctoral dissertation. He postulated that particles may also possess wavelike properties and that these wavelike properties would manifest themselves only in phenomena occurring on an atomic scale, as dictated by Planck s constant. He also postulated that the wavelength of these matter waves, for a given particle such as an electron or proton, would be inversely proportional to the particle s momentum p, which is a product of its mass m and speed... 

Although the quantum theory of 1925 resolved the age-old dilemma of light by unifying the entities of light and matter and by asserting that wave-particle duality applies to both, it failed to address the issue of another fundamental distinction between the two the photon is created out of nothing—in the flash of an atomic jump—while the electron is permanent. 

What experimental evidence supports the quantum theory of light Explain the wave-particle duality of all matter. For what size particles must one consider both the wave and the particle properties ... 

In 1903, Marie Curie, her husband and Henri Becquerel received the Nobel Prize in physics Marie won another Nobel prize (chemistry) in 1911. In 1900, Max Planck had postulated that light energy must be emitted and absorbed in discrete particles, called quanta. In Paris in 1924, Victor de Broglie concluded that if light could act as if it were a stream of particles, particles could have the properties of waves. Both quanta and waves are central to quantum physics. Quantum theory states that energy comes in discrete packets, called quanta, which travel in waves. The principle of wave-particle duality states that all subatomic particles can be considered as either waves or particles. Light is a stream of photon particles that travel in waves. 

Despite the spectacular success of quantum theory in correctly predicting many of those atomic properties that baffled classical physics, the meaning of state functions and the mechanism of so-called quantum jumps between stationary states have remained problematical. The major inhibiting factor has been the reluctance to abandon the classical concept of indivisible point particles as a basis of the wave-like properties of matter. The compromise concepts of wave/particle duality and probability density have stimulated an illogical belief in ghost-like phenomena in order to rationalize quantum behaviour. 

A.D. Quantum mechanics jazzes up all of these theories of the atom by showing that just as traditional wave-like light could be considered a particle, traditional particle-like electrons could be considered like a wave. This wave-particle duality, one... 

In the early twenty-first century it is generally accepted that both the wave and the particle theories are correct in describing optical events. For some optical situations hght behaves as a wave and for others the particle theory is needed to explain the situation. Quantum physics tries to explain the wave-particle duality, and it is possible that future work will unify the wave and particle theories of light. 

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