Wave particle duality

If we think in terms of the particulate nature of light (wave-particle duality), the number of particles of light or other electi omagnetic radiation (photons) in a unit of frequency space constitutes a number density. The blackbody radiation curve in Fig. 1-1, a plot of radiation energy density p on the vertical axis as a function of frequency v on the horizontal axis, is essentially a plot of the number densities of light particles in small intervals of frequency space. 

You can appreciate why scientists were puzzled The results of some experiments (the photoelectric effect) compelled them to the view that electromagnetic radiation is particlelike. The results of other experiments (diffraction) compelled them equally firmly to the view that electromagnetic radiation is wavelike. Thus we are brought to the heart of modern physics. Experiments oblige us to accept the wave-particle duality of electromagnetic radiation, in which the concepts of waves and particles blend together. In the wave model, the intensity of the radiation is proportional to the square of the amplitude of the wave. In the particle model, intensity is proportional to the number of photons present at each instant. 

The difficulty will not go away. Wave-particle duality denies the possibility of specifying the location if the linear momentum is known, and so we cannot specify the trajectory of particles. If we know that a particle is here at one instant, we can say nothing about where it will be an instant later The impossibility of knowing the precise position if the linear momentum is known precisely is an aspect of the complementarity of location and momentum—if one property is known the other cannot be known simultaneously. The Heisenberg uncertainty principle, which was formulated by the German scientist Werner Heisenberg in 1927, expresses this complementarity quantitatively. It states that, if the location of a particle is known to within an uncertainty Ax, then the linear momentum, p, parallel to the x-axis can be known simultaneously only to within an uncertainty Ap, where... 

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 Lewis model of the chemical bond assumes that each bonding electron pair is located between the two bonded atoms—it is a localized electron model. However, we know from the wave-particle duality of the electron (Sections 1.5-1.7) that the location of an electron in an atom cannot be described in terms of a precise position, but only in terms of the probability of finding it somewhere in a region of... 

Quantum description of light the wave/particle duality... 

We are used to thinking of electrons as particles. As it turns out, electrons display both particle properties and wave properties. The French physicist Louis de Broglie first suggested that electrons display wave-particle duality like that exhibited by photons. De Broglie reasoned from nature s tendency toward symmetry If things that behave like waves (light) have particle characteristics, then things that behave like particles (electrons) should also have wave characteristics. 

Tunneling may be conceptualized in several ways. For example, the wave-particle duality of quantum mechanics indicates that particles of mass m and velocity v have an associated de Broglie wavelength given in Eq. 10.6, where h is Planck s constant."... 

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. 

Wave-particle duality The description of matter as a wave or a particle is possible and neither is preferred. Particle-type questions get particle-type answers and wave-type questions get wave-type answers. 

Schrodinger equation valence electrons wave function wavelength, X wave mechanical model wave-particle duality of nature... 

The electron, discovered by J. J. Thomson in 1895, was first considered as a corpuscule, a piece of matter with a mass and a charge. Nowadays things are viewed differently. We rather speak of a wave-particle duality whereby electrons exhibit a wavelike behavior. But, in Levine s own words [45], quanmm mechanics does not say that an electron is distributed over a large region of space as a wave is distributed it is the probability patterns (wavefunctions) used to describe the electron s motion that behave like waves and satisfy a wave equation. 

Electron diffraction In 1924, de Broglie postulated his principle of wave-particle duality. Just as radiation displays particle-like characteristics, so matter should display wave-Uke characteristics. It followed, therefore, from eqs (22) and (2.7) that a particle with energy, E, and momentum, p, has associated with it an angular frequency, , and wave vector, k, which are given by... 

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