December 10, 2005
Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and provides the concrete connections between geometries and trigonometric wavefunctions that observe Pythagorean theorem. By integrating four quaternity space dimensions with conventional Cartesian coordinate systems in calculus, we explain electronic motions by the Maxwell equation and general Stokes theorem from the principles of rotation operation and space and time symmetry. Altogether with the previous reports, we have effectively established quaternity spacetime as a successful theory in elucidating the orbital shapes and motions of electrons within inert atoms such as helium and neon. We point out once again that 2px, 2py, and 2pz orbitals have different geometrical shapes as well as orthogonal orientations, contrary to the traditional 2p orbital model.
Similar papers 1
November 2, 2005
Euclidean geometry does not characterize dynamic electronic orbitals satisfactorily for even a single electron in a hydrogen atom is a formidable mathematical task with the Schrodinger equation. Here the author puts forward a new spacetime concept that regards space and time as two orthogonal, symmetric and complementary quantities. They are inherent physical quantities that cannot be divorced from physical objects themselves. In two-dimensional helium shell, space and time a...
May 30, 2007
Euclidean space and linear algebra do not characterize dynamic electronic orbitals satisfactorily for even the motion of both electrons in an inert helium atom cannot be defined in reasonable details. Here the author puts forward a novel two-dimensional spacetime model from scratch in the context of defining both electrons in a helium atom. Space and time are treated as two orthogonal, symmetric and complementary quantities under the atomic spacetime. Electronic motion observ...
May 31, 2007
In the context of two-dimensional spacetime within a helium atom, both 1s electrons are characterized by wave functions that observe duality equation. They are symmetric, orthogonal and interwoven, forming a dynamic rope structure at any moment. Instead of elliptical orbit of planets around the sun, electronic orbitals take the form of matter state transformation cycle. While the kinematic movement of planets is governed by Kepler's first law, electronic transformation obeys ...
July 18, 2003
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component is then revealed, which reduces part of the degree of freedom found in the gauge, but which can then be used to explain thermoelectricity, suggesting that the theory of heat has just as fundamental a connection to electromagnetism as the m...
June 7, 1998
The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.
August 12, 1992
One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of this process we propose a principle that generalizations of mathematical structures that are already part of successful physical theories serve as good guides for the development of new physical theories. The principle is a more formal presentation and extension of a position stated earlier this century by Dirac. Quaternions form an...
October 16, 2005
This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and identities. This quaternion bibliography will be further updated and corrected if necessary by the authors, who welcome any comment and reference that is not contained within the list.
April 19, 2015
This dissertation is about The history of quaternions and their associated rotation groups as it relates to theoretical physics.
November 30, 2005
This is part two of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and identities. This quaternion bibliography will be further updated and corrected if necessary by the authors, who welcome any comment and reference that is not contained within the list.
January 9, 2021
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many additional possibilities if compared to complex quantum mechanics ($\mathbbm{C}$QM), and thus there are many possible applications to these results in future research.