Abstract Bohr’s theory of the atom did a fine job of explaining the absorption and em1ss10n spectra of one-electron atoms in terms of the quantum rules. Schrodinger’s wave mechanics did better in the sense that the rules of quantization were given a firm mathematical basis. However, problems still abounded. Experimental spectra revealed quite a number of problems for which wave mechanics (and matrix mechanics) appeared to have no solutions. In particular, some atomic emission lines predicted by the theory were seen to be split in the presence of a magnetic field into several quite distinct lines (a phenomenon known as the Zeeman effect). Neither wave mechanics nor matrix mechanics could explain this phenomenon without some further, largely ad hoc, assumptions. Worse still, when the spectra of atoms with two or more electrons were studied, certain predicted lines were found to be missing.
Abstract Bohr’s theory of the atom did a fine job of explaining the absorption and em1ss10n spectra of one-electron atoms in terms of the quantum rules. Schrodinger’s wave mechanics did better in the sense that the rules of quantization were given a firm mathematical basis. However, problems still abounded. Experimental spectra revealed quite a number of problems for which wave mechanics (and matrix mechanics) appeared to have no solutions. In particular, some atomic emission lines predicted by the theory were seen to be split in the presence of a magnetic field into several quite distinct lines (a phenomenon known as the Zeeman effect). Neither wave mechanics nor matrix mechanics could explain this phenomenon without some further, largely ad hoc, assumptions. Worse still, when the spectra of atoms with two or more electrons were studied, certain predicted lines were found to be missing.
The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect (the phenomenon of the deflection of electrons at low speeds being less than at higher speeds in atomic collisions), and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra.
In its beginning, quantum mechanics was approached in two completely different ways. Schrodinger, reasoning that electronic motions could be treated as waves, developed wave mechanics. The stationary states that an electron or molecule might have were analogues to standing waves set up by applying appropriate boundary conditions. Bohr’s theory could not explain the Stark and Zeeman effect, and the spectra of atoms more complex than alkali metals. In 1927, Heisenberg added one more dimension to the problem through the uncertainty principle. The postulates of any theory are a set of fundamental statements that are asked to be believed and draw conclusions from them. In classical mechanics, all dynamical variables are observables, but there are certain fundamental restrictions placed upon simultaneously measurable quantities in quantum mechanics.
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.
The physics community was now faced with two theories of quantum phenomena which could scarcely have differed more radically from one another and yet both had achieved remarkable successes in explaining precisely the same physical phenomena – the spectral lines of the hydrogen atom, the zero point energy of quantum systems, the quantisation of the harmonic oscillator, the quantum rotator and the Stark effect. Furthermore, both theories could account for the experimental data, unlike the predictions of the old quantum theory. Perhaps these quite different approaches are not so surprising when it is appreciated that matrix and wave mechanics started from the diametrically opposite poles of the wave–particle duality. At the heart of the Heisenberg approach was the fundamental role played by the non-commutative behaviour of the quantum variables and the quantisation of both the momentum and spatial variables. To accommodate these features, a new mathematical calculus had been invented from the realisation that matrices followed precisely the correct algebraic rules. The elaboration of this scheme led to the concept of the energy levels of a quantum system being associated with the diagonalisation of matrices using the eigenvalue procedure. As Jammer remarks, the theory ‘… defied any pictorial representation; it was an algebraic approach which, proceeding from the observed discreteness of spectral lines, emphasised the element of discontinuity ; in spite of its renunciation of classical description in space and time it was ultimately a theory whose basic conception was the corpuscle .’
Bohr theory was not satisfactory as it failed to provide an interpretation of relative line intensities and splitting of spectral lines in the presence of electric field and magnetic field in the hydrogen spectrum. This theory also failed completely when it was applied to explain the energies and spectra of more complex atoms. In this chapter, we consider the application of Schrödinger wave theory to one-electron atom. The simplest one-electron system is the Hydrogen atom, whose Schrödinger equation can be exactly solved. Other one-electron system like He + , Li 2+ etc. can also be solved exactly. The chemical system with more than one-electron cannot be solved exactly due to electron-electron repulsion, which is the most problematic term.
Bohr theory was not satisfactory as it failed to provide an interpretation of relative line intensities and splitting of spectral lines in the presence of electric field and magnetic field in the hydrogen spectrum. This theory also failed completely when it was applied to explain the energies and spectra of more complex atoms. In this chapter, we consider the application of Schrodinger wave theory to one-electron atom. The simplest one-electron system is the Hydrogen atom, whose Schrodinger equation can be exactly solved. Other one-electron system like He + , Li 2+ etc. can also be solved exactly. The chemical system with more than one-electron cannot be solved exactly due to electron-electron repulsion, which is the most problematic term.