One way to understand this qualitative failure of classical mechanics is to note that the origin of the problem is our attempt to observe very small deflections as a function of b. As we saw, a deflection arises from momentum transfer in the direction of b. So what we are seeking to do is to measure simultaneously momentum and position in the same direction. The Heisenberg uncertainty principle puts a limit on our inherent ability to do so. When can we no longer [Pg.123]

It is noteworthy that Gibbs himself was acutely aware of the qualitative failures of 19th-century molecular theory (as revealed, for example, by erroneous classical predictions of heat capacities Sidebar 3.8). In the preface to his Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics (published in the last year of his life), Gibbs wrote [Pg.440]

The theoretical basis for classical mechanics, in the form we know it today, was laid by Newton in the seventeenth century. The theory had an unprecedented success in explaining virtually all observed phenomena pertaining to macroscopic systems. The failure of Newtonian mechanics to describe systems on an atomic and molecular scale was not realized to its full extent until toward the end of the nineteenth century, when the atomic structure of [Pg.162]

It is commonly accepted that the old quantum theory era spans from the birth of Planck s quantum hypothesis to the formulation of Schrodinger s equation. This section describes the old quantum theory in three parts the failure of classical mechanics, the birth of the quantum theory, and the completion of wave mechanics.5 8) This century obviously began with the birth of quantum theory. Many researchers appeared on the scene of quantum theory at the time, but we remember mostly the contributions of four researchers Max Planck (1901), Albert Einstein (1905), Niels Bohr (1913), and de Broglie (1923). Then Schrodinger proposed the new wave equation to conclude the age of the old quantum theory. Heisenberg established matrix mechanics and formulated the uncertainty principle. [Pg.21]

Chaos provides an excellent illustration of this dichotomy of worldviews (A. Peres, 1993). Without question, chaos exists, can be experimentally probed, and is well-described by classical mechanics. But the classical picture does not simply translate to the quantum view attempts to find chaos in the Schrodinger equation for the wave function, or, more generally, the quantum Liouville equation for the density matrix, have all failed. This failure is due not only to the linearity of the equations, but also the Hilbert space structure of quantum mechanics which, via the uncertainty principle, forbids the formation of fine-scale structure in phase space, and thus precludes chaos in the sense of classical trajectories. Consequently, some people have even wondered if quantum mechanics fundamentally cannot describe the (macroscopic) real world. [Pg.53]

In the first years of 1900, however, physicists started studying the structure of atoms and soon realised that it was impossible to describe them with models of either particles or waves. Those models were inevitable in classical physics, and their failure could only mean that that physics is not valid at the atomic scale. The laws which apply to one level of reality are not necessarily valid at other levels, but this did not stop the unification process. In the end, quantum mechanics did manage to account for the atomic world, and it turned out that it could also explain the results of classical physics, which means that a bridge can actually be built between different levels of reality. A new synthesis, in other words, became possible because the quantum description of nature was able to contain, as a particular case, the description of classical physics. [Pg.63]

Part 1 of this textbook presents the study of the macroscopic properties of material systems of many molecules, based on thermodynamics. This part of the textbook presents the study of individual atoms and molecules. This study is based on quantum mechanics. Classical mechanics pre-dated quantum mechanics, and this chapter presents both classical mechanics and the so-called Old Quantum Theory, which consists of several theories contrived to explain the failure in the late 1800s of classical mechanics to describe or explain certain molecular phenomena. [Pg.620]

It has been found, however, that the numbers obtained in this way do not agree with experimental determinations of the ionisation and excitation potentials. On this account wc shall refrain from discussing more fully this model for Ha+. At present the reason for the failure of the theory is by no means clear. We shall see later that the treatment of atomic problems with the help of classical mechanics [Pg.245]

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