Models and Modelers of Hydrogen

The following sections are included:

• Preface

• To The Reader

• Contents

Ruminations on waves and particles can be traced back to the Greeks. Thales of Miletus, a wave man, was apparently the first to think of water as the universal and the eternal substrate.

During the 1890s many facts regarding the nature of the atom emerged, the most important being that the atom was composed of even smaller particles. Theoretical and experimental discoveries of the time led to the identification of the first subatomic corpuscle, as J. J. Thomson originally called the electron. The measurement of it's e/m ratio, as well as of the properties of cathode rays, opened up a new perspective of the atom and helped to understand several then unexplained phenomena (e.g., atomic spectra). Reluctant to adopt a planetary view, Thomson deliberately chose an electromagnetic approach that has invoked the image of plum puddings and raisin muffins. Although Thomson's model was unsatisfactory for many reasons, it paved the way for Rutherford, one of his brilliant co-workers.

Early this century Ernest Rutherford established the nuclear model of the hydrogen atom, presently taught as representing the best visual model after modification by Niels Bohr and Arnold Sommerfeld. It replaced the so-called “plum pudding” model of J. J. Thomson which held sway previously. While the Rutherford model represented a large step forward in our understanding of the hydrogen atom, questions remained, and still do.

This essay on the work of Niels Bohr as “modeller of hydrogen” outlines the state of knowledge of the atom in the late 19th and early 20th centuries and details the particular background and discoveries which influenced Niels Bohr in developing his concept of the structure of the atom of hydrogen. It shows that although he was not the first to propose a structure of the atom, he was the first to successfully use the experimental and theoretical developments of the day to produce an atomic structure from which results could be obtained in agreement with experiment. Based on the original paper, the development of the structure of the hydrogen atom is discussed and the difficulties encountered detailed. The original paper by Bohr can be seen as one of the works at the beginning of the application of the quantum concept of Max Planck to natural phenomena other than the emission of light. The limitations of the Bohr model which resulted in its gradual replacement with other models of the atomic structure are discussed.

Arnold Sommerfeld's part in the hydrogen atom story is in large part that of teacher and synthesizer. His book, Atomic Structure and Spectral Lines and it's supplementary volume, Wave Mechanics provided the foundation for most other researchers in the field. His principal original contribution was rewriting the old quantum theory of Niels Bohr into relativistic form and in so doing explained the origin of the fine structure of the hydrogen lines and discovered the fine structure constant.

Samuel Goudsmit reminds us of an exciting period in the history of physics — a period of sweet confusion in the experimental data available and in the theories that attempted to explain them. Hence, physicists were busy — so busy that they did not notice an oddball like Goudsmit was working amongst them. Goudsmit had unusual interests and unusual methods of approaching problems. This is what helped him and Uhlenbeck to come up with the concept of electron spin. Although present day physicists might find electron spin a perfectly natural idea, in 1925 it was strange and unusual. An attempt is made here to follow the historical development of the concept of electron spin as seen by Goudsmit. A current mathematical model is also presented. Finally, Goudsmit's persistent concern about the current directions of young physicists is discussed.

The hydrogen atom is approached from classical physics, starting with basics and evolving into Poisson brackets. Heisenberg entered the quantum world from there. This approach is perhaps better for scattering theory than bound state energy levels, so Heisenberg did not contribute much of direct value to the understanding of quantum hydrogen structure. Schrödinger showed that his and Heisenberg's formalisms are equivalent, so in principle hydrogen could be analyzed using Heisenberg's approach, but not easily.

A brief account is given of some of the main events in Erwin Schrödinger's life, the circumstances leading to his discovery of wave mechanics in 1925–1926, and the application of this mechanics to a model of the hydrogen atom. Two methods of solving this model are outlined, namely, Sommerfeld's polynomial method and Schrödinger's shift operator method. The relation to Pauli's analysis of the quantum-mechanical hydrogen atom is also discussed.

Discovering the non-commutativity of conjugate variables as the most significant feature of Heisenberg's work, Dirac provided a mathematical structure to quantum theory. He then used that formalism to derive Bohr's formula for the hydrogen spectrum and also to develop a quantum theory of radiation wherein he derived the A and B coefficients in terms of which Planck's black-body radiation formula had been obtained by Einstein.

Dirac's greatest achievement was the relativistic equation of the electron, eliminating thereby the ersatz nature of Goudsmit's concept of the electron spin. This equation was applied to predict the energy levels of the hydrogen atom in agreement with Sommerfeld's fine structure formula. This equation also led to the concept of the anti-particle.

In an interview with this book's editor, Hans Sallhofer points out the formal mathematical identity of electrodynamics with wave mechanics. This Maxwell–Dirac isomorphism (MDI) assists him in formulating a model of the hydrogen atom in terms of E‖B fields. Sallhofer criticizes the lack of predictive content in the Copenhagen interpretation of quantum physics, and comments on certain societal issues affecting science.

The following reprint articles are included:

• On the structure of the atom

• The Scattering of α and β Particles by Matter and the Structure of the Atom

• On the Constitution of Atoms and Molecules

• Zur Theorie des Zeeman-Effekts der Wasserstofflinien, mit einem Anhang über den Stark-Effekt

• Spinning Electrons and the Structure of Spectra

• Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik

• Quantisierung als Eigenwertproblem

• The Quantum Theory of the Electron

• The Quantum Theory of the Electron. Part II

• Hydrogen in Electrodynamics. VI. The General Solution

The following sections are included:

• Index