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.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.

Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical CharacterAug 1, 1931100 citations

Diagonal Wave Functions for the Helium Atom.

Melvin Philip Sobol

Jan 1, 19640 citations

Symmetry of the nodal hypersurface for 1s2p P3 helium

James B. Anderson

The wave function for the 1s2p ${\mathrm{}}^{3}$ P state of the helium atom is found to have an unexpectedly simple nodal hypersurface, symmetric about the z axis when the position of one electron is fixed and independent of the interelectron distance. The six-dimensional configuration space of the electrons is divided by the surface into two geometrically similar regions, but the hypersurface is not a plane of symmetry and points on the hypersurface are not at equivalent sites in the two regions.The wave function for the 1s2p ${\mathrm{}}^{3}$P state of the helium atom is found to have an unexpectedly simple nodal hypersurface, symmetric about the z axis when the position of one electron is fixed and independent of the interelectron distance. The six-dimensional configuration space of the electrons is divided by the surface into two geometrically similar regions, but the hypersurface is not a plane of symmetry and points on the hypersurface are not at equivalent sites in the two regions.

Physical Review AApr 1, 198725 citations

PRECISE SCHROEDINGER WAVE FUNCTIONS FOR TWO-ELECTRON ATOMS.

Charles Schwartz

Oct 31, 19690 citations

Hydrogen and helium atoms in strong magnetic fields

Anand Thirumalai, Jeremy Heyl

The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.

arXiv:0806.3113Physical Review AJan 30, 200938 citations

Wave Functions for One and Two Atom Systems.

J. E. Swain

Jan 1, 19640 citations

The wave function for the 1s2p

{\mathrm{}}^{3}

P state of the helium atom is found to have an unexpectedly simple nodal hypersurface, symmetric about the z axis when the position of one electron is fixed and independent of the interelectron distance. The six-dimensional configuration space of the electrons is divided by the surface into two geometrically similar regions, but the hypersurface is not a plane of symmetry and points on the hypersurface are not at equivalent sites in the two regions.