Classical physics definitions

Explosion has several attributes and hence can be described ot defined in different ways- From the standpoint of chemistry it is a rapid cheuircai process resulting in the evolution of gas and heat. To the classic physical definition of a high-pressure energy release must be added thermonuclear effects. Both chemical and physical concepts must be combined to obtain a complete terminology Ref H. Pessiak, Explosivstoffe, 1960, 23—6, 45-7... 

The next section in this chapter provides a brief comparison of the dipole moment (magnitude and direction) for a set of simple alcohols. Experimental gas phase dipole moments45 are compared to ab initio and as molecular mechanics computed values. It is important to note that the direction of the vector dipole used by chemists is defined differently in classical physics. In the former definition, the vector points from the positive to the negative direction, while the latter has the orientation reversed. 

Naturally this coincidence does not mean that the geometric optics added to the classical physics could be used for the exact description of the light propagation since the Michelson-Morley experiment refuted its validity forever. It is evident that there are possible new mathematical definitions for c+ and c instead of the ordinary speed addition mle of the classical physics seen in Eqs. (9) and (11). These can be compatible with the experimental results as well. 

Such considerations led to the early solar-system picture of the atom, in which an electron presumably revolved about the nucleus in one or another definite orbit but was unable to take a position between the orbits when the electron shifted from an outer orbit to an inner orbit, nearer the positively charged nucleus, it would give off the energy detected in the spectra. (It was an open question why an electron would be allowed in one orbit or another and yet be prohibited from taking an intermediate position between the orbits.) Bohr used such a picture and, with classical physical laws, drew up equations that described the supposed motion of the electron in its circular orbit. Using simple assumptions, he successfully explained the structure of the hydrogen spectrum. 

An inevitable consequence of de Broglie s standing-wave description of an electron in an orbit around the nucleus is that the position and momentum of a particle cannot both be known precisely and simultaneously. The momentum of the circular standing wave shown in Figure 4.18 is given exactly hj p = h/, but because the wave is spread uniformly around the circle, we cannot specify the angular position of the electron on the circle at all. We say the angular position is indeterminate because it has no definite value. This conclusion is in stark contrast with the principles of classical physics in which the positions and momenta are all known precisely and the trajectories of particles are well defined. How was this paradox resolved ... 

To understand the behavior of electrons in atoms and molecules requires the use of quantum mechanics. This theory predicts the allowed quantized energy levels of a system and has other features that are very different from classical physics. Electrons are described by a wavefunction, which contains all the information we can know about their behavior. The classical notion of a definite trajectory (e.g. the motion of a planet around the Sun) is not valid at a microscopic level. The quantum theory predicts only probability distributions, which are given by the square of the wavefunction and which show where electrons are more or less likely to be found. 

There is a definite possibility of using classical physical quantities under operator companions, that is, an approach to quantization [ 19]. If a classical quantity was expressed by a function// , q) of the canonical variables, p, q, the Fourier transform of/can be used. Then,/is back-transformed from by... 

Recall that in classical physics, by definition, the angular momentum of a particle is the vector L = [r X mv], where r is the position vector of the particle relative to the origin, m is the mass of the particle, and v is the velocity of the particle. 

If the expression the size of an atom is to have any meaning, it must have something to do with the distance between the electron and the nucleus. Several definitions are possible at this stage we choose to identify the atomic radius with the maximum distance allowed by classical physics, equation (1.7) ... 

This means that the probability density of an electron in a orbital of a one-electron atom falls to zero only as r approaches inUnity. As we have seen above, classical physics leads to the conclusion that an electron with < 0 will be unable to move further away from the nucleus than the distance at which the total energy of the electron is equal to the potential energy. According to quantum mechanics there is a definite probabiUty of... 

This illustrates the link between time, symmetry, and energy conservation, which is a great principle in classical physics. It also outlines the importance of defining the validity domain of any invariance rule or principle and that the notion of reversibility depends on the definition of time. 

In classical physics, a moving particle has a definite location at any instant, whereas a wave is spread out in space. If an electron has the properties of both a particle and a wave, can we determine its position in the atom hi 1927, the German physicist Werner Heisenberg postulated the uncertainty principle, which states that it is impossible to know simultaneously the position and momentum (mass times speed) of a particle. For a particle with constant mass m, the principle is expressed mathematically as... 

In the first few chapters we shall discuss some simple, but important, particle systems. This will allow us to introduce many basic concepts and definitions in a fairly physical way. Thus, some background will be prepared for the more formal general development of Chapter 6. In this first chapter, we review briefly some of the concepts of classical physics as well as some early indications that classical physics is not sufficient to explain all phenomena. (Those readers who are already familiar with the physics of classical waves and with early atomic physics may prefer to jump ahead to Section 1-7.)... 

The deformed charge distribution is generally axially symmetrical and this fact has an important consequence. It permits to characterize the charge distribution asymmetry by means of only one quantity, Q (called the quadrupolar moment), even if the quadrupolar operator, is a 3x3 matrix (in classical physics, a quadrupole is a second rank tensor). The definition of Q and the explicit form of are given in references 2 and 3. 

Newton, the limit h —> 0 is singular. The symmetries underlying quantum and classical dynamics - unitarity and symplecticity, respectively - are fundamentally incompatible with the opposing theory s notion of a physical state quantum-mechanically, a positive semi-definite density matrix classically, a positive phase-space distribution function. 

If quantum mechanics is really the fundamental theory of our world, then an effectively classical description of macroscopic systems must emerge from it - the so-called quantum-classical transition (QCT). It turns out that this issue is inextricably connected with the question of the physical meaning of dynamical nonlinearity discussed in the Introduction. The central thesis is that real experimental systems are by definition not isolated, hence the QCT must be viewed in the relevant physical context. 

The possibility to have metastable hadronic stars, together with the feasible existence of two distinct families of compact stars, demands an extension of the concept of maximum mass of a neutron star with respect to the classical one introduced by Oppenheimer Volkoff (1939). Since metastable HS with a short mean-life time are very unlikely to be observed, the extended concept of maximum mass must be introduced in view of the comparison with the values of the mass of compact stars deduced from direct astrophysical observation. Having in mind this operational definition, we call limiting mass of a compact star, and denote it as Mum, the physical quantity defined in the following way ... 

Lavoisier s dictum that physics should precede chemistry became a logicohistorical interpretation, as he meant it to be, instead of a statement of pedagogical or disciplinary strategy. Paradoxically, the contemporary prestige of physics is associated with this logicohistorical tradition and with the classical and aesthetic appeal of abstract mathematics, rather than with the precision laboratory tradition on which much of modern physics, like chemistry, is based. The founder myth of Lavoisier has been perpetuated in the hagiography of the disciplinary clan of chemistry because of his role not only in the conceptual and linguistic foundations of nineteenth-century chemistry but also in a community of practitioners who refined the social definition of the chemical discipline its formal distinction from "physique" in the Paris Academy, its autonomous status as the subject of the Annales de Chimie, its Janus-faced position astride the abyss that previously divided the philosophical science of the university from the technical practice of the laboratory. 

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