Quantum light theory basis

Whilst the above is perfectly adequate for the description of processes observed with continuous-wave (cw) input, proper representation of the optical response to pulsed laser radiation requires one further modification to the theory. It is commonly thought difficult to represent pulses of light using quantum field theory indeed, it is impossible if a number state basis is employed. However by expressing the radiation as a product of coherent states with a definite phase relationship, it is relatively simple to construct a wavepacket to model pulsed laser radiation [39]. The physical basis for this approach is that pulses necessarily have a finite linewidth and therefore in fact entail a large number of radiation modes, so that for the pump radiation, it is appropriate to construct a coherent superposition... 

A diagrannnatic approach that can unify the theory underlymg these many spectroscopies is presented. The most complete theoretical treatment is achieved by applying statistical quantum mechanics in the fonn of the time evolution of the light/matter density operator. (It is recoimnended that anyone interested in advanced study of this topic should familiarize themselves with density operator fonnalism [8, 9, 10, H and f2]. Most books on nonlinear optics [13,14, f5,16 and 17] and nonlinear optical spectroscopy [18,19] treat this in much detail.) Once the density operator is known at any time and position within a material, its matrix in the eigenstate basis set of the constituents (usually molecules) can be detennined. The ensemble averaged electrical polarization, P, is then obtained—tlie centrepiece of all spectroscopies based on the electric component of the EM field. 

In this chapter we give a brief review of some of the basic concepts of quantum mechanics with emphasis on salient points of this theory relevant to the central theme of the book. We focus particularly on the electron density because it is the basis of the theory of atoms in molecules (AIM), which is discussed in Chapter 6. The Pauli exclusion principle is also given special attention in view of its role in the VSEPR and LCP models (Chapters 4 and 5). We first revisit the perhaps most characteristic feature of quantum mechanics, which differentiates it from classical mechanics its probabilistic character. For that purpose we go back to the origins of quantum mechanics, a theory that has its roots in attempts to explain the nature of light and its interactions with atoms and molecules. References to more complete and more advanced treatments of quantum mechanics are given at the end of the chapter. 

Schrodinger s equation is widely known as a wave equation and the quantum formalism developed on the basis thereof is called wave mechanics. This terminology reflects historical developments in the theory of matter following various conjectures and experimental demonstration that matter and radiation alike, both exhibit wave-like and particle-like behaviour under appropriate conditions. The synthesis of quantum theory and a wave model was first achieved by De Broglie. By analogy with the dual character of light as revealed by the photoelectric effect and the incoherent Compton scattering... 

Classical Newtonian mechanics assumes that a physical system can be kept under continuous observation without thereby disturbing it. This is reasonable when the system is a planet or even a spinning top, but is unacceptable for microscopic systems, such as an atom. To observe the motion of an election, it is necessary to ilium mate it with light of ultrashort wavelength (gamma rays) momentum is transferred from the radiation to the electron and the particle s velocity is. therefore, continuously disturbed. The effect upon a system of observing it can not be determined exactly, and this means that the state of a system at any time cannot be known with complete precision. As a consequence, predictions regarding the behavior of microscopic systems have to be made on a probability basis and complete certainty can rarely be achieved. This limitation is accepted and is made one of the foundation stones upon which the theory of quantum mechanics is constructed. 

Quantum Theory — The basis for understanding atoms and molecules and the production of light. 

The photoelectron effect was first discovered by Henrich Hertz [11] in early 1887 in order to verify the implications of Maxwell s theory and relations. Hertz noticed a spark of light on metal contacts in electrical units when exposed to light. The dawn of a new era actually came in 1905. Albert Einstein brilliantly utilized Planck s new quantum energy concept to explain how low radiation intensity and high frequency can actually eject electrons from a metal piece. The converse failed to produce any electrons. Max Planck received the Nobel Prize on quantization of energy [12] in 1918 and Einstein received the Nobel Prize on photoelectric effect in 1921. The single relationship proposed so long ago by Einstein is still today the fundamental basis of photoelectron spectroscopy,... 

Experience has shown that a quantitative description of the properties of atomic systems is not possible on the basis of the laws of classical physics. Quantum physics represents an attempt at a generalisation of these laws in the sense that a certain constant, Planck s constant, has a finite value A== 6 55.10 erg sec in contrast to classical physics, corresponding to the limit A=0, just as relativistic physics is a generalisation of non-relativistic physics, the latter arising from the former by passing from a finite value of the velocity of light c to an infinite value. Quantum physics in its present form appears adequate for dealing with all questions in which the internal constitution of the electron and the atomic nuclei as well as the theory of relativity need not be taken into ac-... 

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