The spectrum of neutral helium . It is well known that the spectral terms of helium can be divided into two sets such that no term of the one will combine with a term of the other to produce a spectral line. Both sets are approximately like hydrogen terms. One set by its transitions gives the ‘para helium’ lines and consists of singulet terms and to it belongs the ‘normal state’ 1s; the other set gives the ‘ortho helium’ lines and (apart from the singulet terms) consists of very narrow doublets (theory suggests that these are probably triplets). The energies of the ortho terms are slightly higher than those of the corresponding para terms. On account of these two sets of lines, helium had been thought to be a mixture of two gases, para and ortho helium. Many attempts were made to give the theory of these spectra on the earlier quantum theory, both for normal and excited helium, but all failed to give results even in tolerable agreement with experiment. The obvious failure of the classical mechanics and the correspondence principle to solve the problem of a nucleus with two outer electrons was one of the factors which compelled Heisenberg to seek for a new quantum mechanics of discontinuous processes to replace the older theory.
The spectrum of neutral helium . It is well known that the spectral terms of helium can be divided into two sets such that no term of the one will combine with a term of the other to produce a spectral line. Both sets are approximately like hydrogen terms. One set by its transitions gives the ‘para helium’ lines and consists of singulet terms and to it belongs the ‘normal state’ 1s; the other set gives the ‘ortho helium’ lines and (apart from the singulet terms) consists of very narrow doublets (theory suggests that these are probably triplets). The energies of the ortho terms are slightly higher than those of the corresponding para terms. On account of these two sets of lines, helium had been thought to be a mixture of two gases, para and ortho helium. Many attempts were made to give the theory of these spectra on the earlier quantum theory, both for normal and excited helium, but all failed to give results even in tolerable agreement with experiment. The obvious failure of the classical mechanics and the correspondence principle to solve the problem of a nucleus with two outer electrons was one of the factors which compelled Heisenberg to seek for a new quantum mechanics of discontinuous processes to replace the older theory.
Abstract A theory of the helium atom was developed by Heisenberg, following his famous principle of “resonance.” His work is based upon Schrodinger’s equation, and in order to allow for the spin of the electrons he introduces extra energy terms, expressing the classical energy of two appropriate magnets. It is the perturbation by this spin energy which produces the triplet separations. Heisenberg’s calculation of these separations is open to three criticisms: (1) He assumes that certain simple forms are correct first approximations to the wave-functions; whereas, owing to degeneracy, it is necessary to take linear combinations of these forms. (2) He estimates the mean values of the spin energy by means of a model built up of precessing vectors. (3) He neglects the radius of the inner orbit in comparison with that of the outer orbit, even when the principal quantum number of the latter is only 2; this is the least satisfactory of several necessary simplifications. Schrödinger’s equation is likely to be supplanted as the foundation of wave-mechanics by the equation recently put forward by Dirae. This fits the spin of the electron neatly into the theory of relativity, and produces the doublets of the hydrogen-like atom in a beautiful manner. Dirac’s q-number theory has been translated into wave-mechanics by Darwin. Apart altogether from the above criticisms of Heisenberg, it seemed expedient to proceed to the theory of an atom with two electrons on the basis of the new equation. Calculations which are independent of the spin, such as the approximate energylevels, and the separation between ortho- and para-terms, are the same on either theory, and are not the concern of this paper. We deal here with spin effects, such as the fine structure of the triplets and intercombinations between ortho- and para-states.
Helium provides the simplest, multi-electron, atomic situation. Quantum mechanics addresses the different magnetic and spectral properties of ortho and para helium with “mirrored twin” electrons. This paper addresses that difference with “mirrored rooms” and no electron spin-reversed pairing in the same orbital – a different implementation of parity. Models are provided to illustrate why each form of helium can not be converted to the other in a single photon-induced step. These models also illustrate the vastly greater orbital sizes of the excited states over the ground state. Included is a reference to a paper demonstrating that classical physics provides the physical mechanism that explains why an electron’s energy levels scale with the square of integers. The mirror-room orbitals would also be appropriate for non-classical approaches without requiring spin-reverse pairing of electrons in the same orbital.
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.
Abstract We consider three topics which proved frustratingly resistant to the methods of the old quantum theory up to the point of emergence of the quantum mechanics of Heisenberg and collaborators in late 1925. First, the old theory could not account convincingly for the superfluity of stationary states implied by the existence of the complex multiplets seen in most atomic spectra. Second, the progressively more complicated theories proposed for explaining the splittings of lines in the anomalous Zeeman effect were found to lead inevitably to glaring inconsistencies with the assumed mechanical equations of motion. Finally, there was the problem of the dual spectrum of helium, and even more basically, of the ground state energy of helium, all calculations of which in terms of specified electron orbits gave incorrect results. We relate the tangled history of the efforts to provide a theoretical resolution of these problems within the old quantum theory.
Abstract 1. The chief object of the present paper is to present a simple system of equations which are competent to determine the frequencies and intensities of the lines in the standard Zeeman effect. By the standard Zeeman effect is meant the type where the terms are given by Landé’s "g"and “γ” formulæ, and where the multiplicity of the two sets of terms is the same. It will probably be held that the theory of such multiplets has been fairly completely understood for the last two years owing to the works of Sommerfeld, Heisenberg, Landé and Pauli, and the main new contribution of the present work is that, whereas these writers gave formulæ valid only either in weak or strong field (except for doublets, where Heisenberg and Jordan give the value for any strength), here we have complete formulæ from which the intensity of any component in any strength of field can be obtained merely from the solution of rather simple algebraic equations. The proper attack on this problem would undoubtedly be by way of the recent work of Heisenberg on the helium spectrum, and his still more recent work on complex spectra; but this theory is still in the making, so that it has not been practicable to apply it here, and to this extent our results are unverified. Their validity rests firstly on a complete verification of all known facts connected with both weak and strong fields (and intermediate fields for doublets), and also on a conformity with the general features of wave mechanics. The work of Heisenberg and Jordan could readily have been adapted to give all the results of the present paper; but it would have been harder to follow because the matrix methods are not so easy for most readers as are spherical harmonics.
Abstract One of the outstanding differences between classical theory and quantum mechanics is the importance which the latter attaches to the identity of particles. Although perfectly well realised before the introduction of modern quantum theory, the fact that two electrons are experimentally indistinguishable did not introduce any novel features into the dynamics of many electron systems on Bohr’s theory. However, Heisenberg showed that these identity relations are of fundamental importance in many body problems, and was able to explain the formerly very puzzling characteristic of the spectrum of neutral helium, its division into two non-combining term systems. Owing to the identity of the particles, the wave function representing such a system must have certain symmetry properties; for the particles known in Nature this symmetry characteristic is that the function be either symmetric or anti-symmetric in the co-ordinates of the particles. For particles with a spin such as the electron and proton, only antisymmetry is allowed (Pauli’s principle), while for α-particles the wave function must be symmetrical. Since Heisenberg’s explanation of the helium spectrum the theory of anti-symmetric electron wave functions has been extended to describe the general features of the spectra of all atoms, while it appears from the work of Heitler and London that the theory is of fundamental importance in the explanation of chemical combination between atoms. Again, in furnishing a new statistics it is an essential feature of the theory of metals. As the effect of the identity relations depends on the fact that exchanging the electrons does not alter the system in any way, these effects are known as exchange phenomena.