Wolfang Pauli wrote that he had gone by train to pay a visit to Niels Bohr and at the very moment of the accident in James Frank’s laboratory his train stopped for a few minutes in Gottingen station. If, before Bohr, spectroscopy was an essentially empirical science that went little farther than to catalogue absorption and emission wavelengths, the new atomic theory offered a guide to the interpretation of the experimental results and, as often happens, theory and experiment cooperated with each other to yield the interpretation of various observed phenomena. Bohr then turned his attention to molecules, obtaining correct results for the hydrogen molecule but surprisingly not so for the helium atom which also has two electrons. Otto Stern and his collaborators investigated fundamental points concerning the kinetic theory of gases, verified spatial quantization, measured the magnetic moment of the proton, verified the de Broglie relation for waves made by helium atoms etc.
Wolfang Pauli wrote that he had gone by train to pay a visit to Niels Bohr and at the very moment of the accident in James Frank’s laboratory his train stopped for a few minutes in Gottingen station. If, before Bohr, spectroscopy was an essentially empirical science that went little farther than to catalogue absorption and emission wavelengths, the new atomic theory offered a guide to the interpretation of the experimental results and, as often happens, theory and experiment cooperated with each other to yield the interpretation of various observed phenomena. Bohr then turned his attention to molecules, obtaining correct results for the hydrogen molecule but surprisingly not so for the helium atom which also has two electrons. Otto Stern and his collaborators investigated fundamental points concerning the kinetic theory of gases, verified spatial quantization, measured the magnetic moment of the proton, verified the de Broglie relation for waves made by helium atoms etc.
The aim of Niels Bohr’s “great” paper was to try to explain how Ernest Rutherford’s planetary model of the atom could exist. Bohr never used the words “quantum jump” in the paper, but it became very much in vogue shortly after this. Max Planck and even A. Einstein had not yet made the full evolution beyond classical physics, and the purely classical atomic views of Rutherford and H. Nagaoka did not provide the explanation of the absorption and emission spectra of hydrogen. In truth, Bohr’s “theory” consisted of a very few equations, with very great assumptions. As de Broglie’s work became known, he was hailed for his advances and he would join the list of Nobel Prizes for advances in quantum theory. Wolfgang Pauli did not particularly like the wave and particle approach that de Broglie introduced with his pilot waves in 1924, and would forcefully express these objections a few years later at the Solvay conference.
Toward the end of the nineteenth century, it became clear that some experiments cannot be explained on the basis of known physics, now referred to as classical physics. In 1900, Max Planck was able to correctly describe the distribution of blackbody radiation energy as a function of wavelength λ or frequency ν = c/λ. He had to accept the existence of energy packets (quanta) with energy E = hν. A few years later, Albert Einstein found that this unexpected relation between energy and frequency is also necessary in order to understand photoemission from metallic surfaces. A decade later, Niels Bohr arrived at the correct equation for the electronic spectrum of the hydrogen atom by applying “quantum conditions” on the motion of the electron around the nucleus and the Planck’s relation E = hν on the energy difference between the energy levels (1916). A decade later, Heisenberg, Born, and Jordan introduced “quantum mechanics” and de Broglie and Schrödinger (1925-1926) introduced “wave mechanics.”
Meanwhile, on 18 September 1931, Heisenberg wrote to Bohr that ‘my work seems to be somewhat gray on gray’ (Pauli, 1985). By 1931 the bright future for quantum physics that seemed just over the horizon in the fall of 1927 paled with the formulation of relativistic quantum mechanics. Besides the as yet uninterpreted negative energy states, there was the electron's divergent self-energy and the continuous energy spectrum of β-particles in the supposedly two-body final state of nuclear β-decay, which implied that energy was not conserved in nuclear reactions (Bohr, 1932) and that perhaps quantum mechanics was not valid within the nucleus (to be discussed in Chapter 5). Measurement problems in a quantum theory of the electromagnetic field At the 20–25 October 1930 Solvay Conference, Bohr, Dirac, Heisenberg and Pauli concurred that fundamental difficulties in quantum electrodynamics might be clarified by investigating measurability of electromagnetic field quantities. Upon his return to Copenhagen from Brussels, Bohr continued discussing field measurements with Lev Landau, who happened to be visiting at Bohr's institute. In December 1930 Landau went on to Zürich, where he interested Pauli's assistant Rudolf Peierls in field measurements. Their deliberations led to a joint 1931 publication entitled ‘Extension of the uncertainty principle to relativistic quantum theory’ (Landau and Peierls, 1931). Measurement of an electric field can be accomplished through measuring the change in momentum of a charged test body placed in the field.
Rutherford thought to explore the structure of matter by bombarding thin sheets of metals with alpha particles. According to Bohr, the mechanism of emission of e.m. wave is represented by the downward vertical lines connecting states at different n. The two main successes are: explanation of Rydberg formula and expression of Rydberg empirical constant in terms of fundamental constants and the calculation of the size of the atom in agreement with measurements. The remarkable fact that de Broglie hypothesis of pilot waves, when applied to the hydrogen atom, gives excellent agreement with Bohr's theory seems to give foundation that the matter-wave duality is a characteristic of elementary particles like the electrons. Shortly after de Broglie suggestion an experimental verification of de Broglie ideas was successfully attempted. Davisson and Germer needed to choose a crystal whose spacing was such that, under a reasonable acceleration voltage of the electrons, the de Broglie wavelength would be of the order of the lattice spacing.
Thus far we have concentrated on the postulates, on their ramifications, and on the means and methods by which they are applied. Connections with classical physics have been featured, and primary notions other than those of Chapter 5 have not been needed. We deviate from this path in the present chapter, introducing a new and extremely important concept; it is based on one of the most significant and fruitful experiments of the quantal era. This experiment was performed by O. Stern and W. Gerlach (1921) and subsequently interpreted by G. Uhlenbeck and S. Goudsmit (1925). The experiment and its elucidation led to the new concept of “intrinsic spin” (in particular to spin “½”), a development that was one of the major turning points in modern physics. The consequences have been monumental, and include primary theoretical developments; the interpretation of data related to, and an understanding of, empirical rules concerning a wide variety of physical systems (e.g., the periodic table of the elements/atomic structure); and the generation of new experimental techniques and of innovative measurements. Our study of intrinsic spin and its correlative, two-state systems, introduces the reader to one of the most profound topics in quantum theory. The Stern–Gerlach experiment and its interpretation The experiment of Stern and Gerlach was designed to test the “spatial quantization” of neutral atoms, i.e., to determine whether the (orbital) angular momentum was quantized. The basic ideas are as follows. Associated with the atom's orbital angular momentum would be a magnetic moment, as in the Bohr model of hydrogen.
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.