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.
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.
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.
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.
Introduction Helium is the natural connection between the hydrogen-like atoms (one electron outside a spherical core, such as the alkali-metal atoms of Chap. 10) and all the others in the periodic table. For these one-electron atoms the field-free description of the electron motion in terms of three quantum numbers n , ℓ , and m suffices. The other electrons are considered to form the “core” and its effect on the energy levels is reduced to the quantum defects δ ℓ , as discussed in Chap. 10. The case of helium is very different since the two ground-state electrons are in the same electronic state and differ only in the orientation of their spins. Thus spin is of paramount importance for the description of all but the hydrogenic atoms. Since helium has only two spins to deal with, their roles can be written explicitly. Because the two electrons are identical, quantum mechanics requires that the wavefunction undergoes nothing more than an unobservable phase shift when they are exchanged. This consequence is called the Pauli symmetrization principle, and is sometimes referred to as “the source of our individuality”. Moreover, it has a profound influence on the wavefunction and thus on the allowed energy states. It will be shown that this symmetry requirement dictates that two electrons cannot be in states with identical quantum numbers, and this topic will be discussed in detail in this chapter. Symmetry The profound difference between the hydrogen and helium wavefunctions arises because the two electrons are indistinguishable, and this results in a fundamental change of the energy-level structure. The concept of “spin”, introduced as a shortcut for the intrinsic magnetic moment of the electron in Chap. 7, now becomes a dominating feature of the description. Before discussing the helium energy levels, the effects of this symmetry with respect to exchange of identical particles is presented. The exchange operator In quantum mechanics, identical particles are inherently indistinguishable, so the exchange of the two electrons cannot change any observable and there should be no measurable effect on the overall wavefunction. However, there can be an overall phase change whose nature can easily be found by defining an operator P 12 that exchanges the electrons and applying it to the wavefunction. The exchange applies to all coordinates of the electron including its spin coordinate, but for simplicity only the spatial coordinate will be indicated here.
The original intention of the author’s preoccupation with the quantum-mechanical behaviour of simple atoms and molecules such as Hydrogen and Helium was, on the one hand, the elegant simplicity of Niels Bohr’s atom model for Hydrogen, describing the metastable states of the excited electrons by planar concentric electron orbits, and, on the other hand, the hardly intelligible wave mechanical approach of Heisenberg, Schrödinger and others, describing mainly atoms with multiple electrons by three-dimensional orbitals which were characterized by probabilities of presence. Thereby the question arose whether it would be possible to find alternative atom models with well-defined electron trajectories. Therein, Louis de Broglie’s thesis of the wavy nature of electron motion implicating standing waves would have to be implemented. Nevertheless, as reviewed in the introduction, the orthodox three-dimensional concept influenced the own thinking in such a way that three-dimensional constellations for the electronic excited states were conceived. The break-through was achieved for the electronic ground state in the form of the spin-orbit coupling where the spin acts as a perpetuum mobile, inducing the orbital angular momentum h/2π. Furthermore, the insight was gained that a circularly rotating electron intrinsically corresponds to a harmonic oscillator, thus fulfilling the condition of a standing wave. Based on this concept, a double planar model was established for the H2-molecule which could be empirically verified by X-ray data from literature. However, for the two electrons containing Helium a 2D-array seemed impossible since the Pauli-principle seemed to be violated. After a long stepwise succession of 3D-attempts which turned out to be impossible—not least since eccentric forces are not possible in such a system—the here presented 2D-version for Helium was found, composed by two imaginary orthogonal electron orbits. It will enable in a subsequent publication the quantum mechanical interpretation of the thermal-radiative behaviour of Helium which was reported in the author’s publication nine years ago.
The spdf-based orbital theory is a sophism. Things must be declared "different" at the electronic level to renounce classical physics. This paper shows that classical physics still operates at the electronic level! Electron particles are always there. Mass-to-wave/energy conversion and its reversal (duality) on-demand does not actually exist - a ruse that cloaks the negative-negative waive. There is no electron spin-reversal - a gimmick with "nmls" not even consistent orthogonality. The MCAS Way describes the behavior of electrons while preserving their wholeness, mutual orthogonality, and interactive adaptivity. Electrostatics of some simple molecules modeled the MCAS Way are presented. The orbital extent of an electron is shown to be finite while its electrostatic presence stretches to infinity. Electrons hardly ever occupy the region on the axis between two nuclei of a molecule. Excellent correspondence of NMR proton shift with the magnitude of the electrostatic field at the proton is found. Wholly integer quantum numbers identify the orbital spaces of an atom. Electrons do not have quantum numbers! The electron of the hydrogen atom is assigned the 11111 orbital; those of helium are in the 11111 and 11-111 orbitals; and so on. Unlike the static spdf designation, an electron moves to a different type orbital with sufficient electron loading of a shell! A quantum theory does not need duality! The current one, however, needs a different base model to treat particulates. Bimolecular substitution reactions are shown to be path-dependent with an electron transferred in the Transition State. Traditional microscopic reversibility is trashed.
Quantum mechanics (QM) and quantum electrodynamics (QED) are often touted as the most successful theories ever. In this paper, this claim is critically evaluated by a test of internal consistency for the ability to calculate the conjugate observables of the nature of the free electron, ionization energy, elastic electron scattering, and the excited states of the helium atom using the same solution for each of the separate experimental measurements. It is found that in some cases quantum gives good numbers, but the solutions are meaningless numbers since each has no relationship to providing an accurate physical model. Rather, the goal is to mathematically reproduce an experimental or prior theoretical number using adjustable parameters including arbitrary wave functions in computer algorithms with precision that is often much greater (e.g. 8 significant figures greater) than possible based on the propagation of errors in the measured fundamental constants implicit in the physical problem. Given the constraints of adherence to physical laws and internal consistency, an extensive literature search indicates that quantum mechanics has never solved a single physical problem correctly including the hydrogen atom and the next member of the periodic chart, the helium atom. Rather than using postulated unverifiable theories that treat atomic particles as if they were not real, physical laws are now applied to the same problem. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of − e moving in the Coulombic field of the proton and the wave equation as modified after Schrodinger, a classical approach is explored which yields a model which is remarkably accurate and provides insight into physics on the atomic level. The proverbial view deeply seated in the wave-particle duality notion that there is no large-scale physical counterpart to the nature of the electron is shown not to be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantum atomic problems. Specifically, a theory of classical quantum mechanics (CQM) was derived from first principles as reported previously [1-7] that successfully applied physical laws to the solution of atomic problems that has its basis in a breakthrough in the understanding of the stability of the bound electron to radiation. Rather than using the postulated Schrodinger boundary condition: “ 0 Ψ→ as →∞ r ,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound 1 = n -state electron cannot radiate energy. Although it is well known that an accelerated point particle radiates, an extended distribution, modeled as a superposition of accelerating charges, does not have to radiate. A simple invariant physical model arises naturally wherein the predicted results are extremely straightforward and internally consistent requiring minimal math as in the case of the most famous equations of Newton, Maxwell, Einstein, de Broglie, and Planck on which the model is based. No new physics is needed; only the known physical laws based on direct observation are used. The accurate solution of the helium atom is confirmed by the agreement of predicted and observed conjugate parameters using the same unique physical model in all cases.