7 papers
Conjugate Spinor Solution of the Dirac Equation for the Hydrogen Atom
Robert J. Ducharme
It is shown the central field Dirac equation can be simplified through the use of real conjugate spinors to substitute for the upper and lower components of the bi-spinor eigensolu…
Integral Transforms in Relativistic Quantum Constraint Mechanics
Robert J. Ducharme
In relativistic quantum constraint mechanics the state of a physical system is constrained to a 3-dimensional subspace of Minkowski 4-space. Fourier transformation can be used to r…
Isometric Entanglement of Particle Positions in Quantum Bound Systems
Robert J. Ducharme
It is shown the role of a scalar potential in the Schrödinger equation for a steady-state two-particle system is equivalent to an isometric entanglement of the position coordinates…
Exact Solution of the Klein-Gordon Equation for the Hydrogen Atom Including Electron Spin
Robert J. Ducharme
The term describing the coupling between total angular momentum and energy-momentum in the hydrogen atom is isolated from the radial Dirac equation and used to replace the correspo…
Conformal Mapping of Relativistic Quantum Bound Systems to Eliminate Potential Fields
Robert J. Ducharme
In two recent papers, an isometric conformal transformation has been introduced that eliminates potential interaction terms from the Schrödinger equation for central potential prob…
Conformal Transformation of the Schrödinger Equation for Central Potential Problems in Three-Dimensions
Robert J. Ducharme
In a recent paper, it has been shown the Schrödinger equation for the three-dimensional harmonic oscillator can be simplified through the use of an isometric conformal transformati…