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CRC Press eBooks

Quantum Theory I

Sadri Hassani

Published May 7, 2010• 0 citations
Publisher

Abstract

Bohr’s model of the hydrogen atom was a hybrid between the classical Newtonian physics and the radical idea of the quantization of light. Newtonian physics by itself failed miserably when encountered with an atom that had a nucleus, and when Bohr mixed it with a dab of modern physics, it was improved; but only partially. It appeared that Newtonian physics needed a dramatic metamorphosis.

DOI
10.1201/9781439882849-31

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Cambridge University Press eBooks•Jul 20, 2009•0 citations
Bohr’s model of the hydrogen atom was a hybrid between the classical Newtonian physics and the radical idea of the quantization of light. Newtonian physics by itself failed miserably when encountered with an atom that had a nucleus, and when Bohr mixed it with a dab of modern physics, it was improved; but only partially. It appeared that Newtonian physics needed a dramatic metamorphosis.
The world should have waited until 1913, when a Danish physicist N. Bohr proposed an entirely new theory for a description and partial explanation of the spectral properties of the hydrogen atom. His theory was based on two postulates, the so-called Bohr postulates, and both of them were impossible to be understood from the point of view of classical physics. Being based on these postulates and employing classical physics, N. Bohr was able to derive explicit expressions for the energy levels of the hydrogen atom and the wavelengths of possible transitions. The hydrogen-like atom has only one electron, and all others have been removed by various ways of ionization. An essential feature of these systems is the presence of one electron only. The Coulomb interaction between this electron and the nucleus is spherically symmetrical. Later, we shall see that the situation becomes considerably more complicated in the case of multielectron atoms.
Through his experiments, the physicist Niels Bohr improved upon Rutherford's model of the atom and developed his model of the atomic structure in 1913 that succeeded in explaining the spectral features of the hydrogen atom. A simple means for extending the conventional non-relativistic Bohr model of the atom to include the wave nature of electrons is presented. As the derivation requires basic knowledge of classical and wave mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics.
Chapter 2 explains how in constructing quantum mechanics, old ideas had to be discarded and well-established principles had to be modified or even abandoned. First it was necessary to be convinced of the physical reality of the atomic structure of matter; then to show that Newtonian mechanics is not directly applicable to the study of the atom; later to show that Maxwell’s electrodynamics alone does not describe all the elementary processes of interaction between an atom and other quantum particles. The chapter takes us from Planck’s energy quantum to Einstein’s quantization as a universal phenomenon, from Bohr’s quantum atom model, and the early quantization rules, to de Broglie’s waves associated with corpuscles in motion. It ends with a corollary on the electrodynamic nature of quantum mechanics.
The purpose of this work is to retrace the steps that were made by scientists of XX century, like Bohr, Schrodinger, Heisenberg, Pauli, Dirac, for the formulation of what today represents the modern quantum mechanics and that, within two decades, put in question the classical physics. In this context, the study of the electronic structure of hydrogen atom has been the main starting point for the formulation of the theory and, till now, remains the only real case for which the quantum equation of motion can be solved exactly. The results obtained by each theory will be discussed critically, highlighting limits and potentials that allowed the further development of the quantum theory.
The new physics just described was still based largely on Newtonian ideas. Indeed, in its theoretical aspects, it might not unfairly be described as a final attempt to explain the world in materialistic terms—as particles being pushed and pulled about in space and time. Nevertheless, the new physics had found it necessary to abolish most of the forces of pushing and pulling, replacing the gradual changes of motion of the particles under these forces by sudden and unpredictable jumps. These appeared to involve violations of the law of causality, both in the disintegration of radioactive atoms and also in the internal changes of ordinary atoms. We seemed to see Fate defying this law as she picked out certain atoms for disintegration or collapse and, by her apparently capricious acts, sent the universe along one path or another according to her whim. On such lines the new physics had explained many phenomena which had hitherto seemed inexplicable, but it had by no means met with complete success. For instance, while it gave a perfect interpretation of the simplest spectrum of all, namely that of the hydrogen atom, it failed with more complex spectra. This was not necessarily a fatal objection; a few emendations and possibly a few new ad hoc assumptions might have effected a complete reconciliation, although this seems improbable.