Schrödinger equation for a dirac bubble potential

Chr. Klixbüll Jørgensen

Abstract In Schrödinger's equation, the local contribution to the kinetic energy is sometimes negative, but it allows a conservative potential in contrast to an alternative, never negative, energy proposed by Ruedenberg. The total kinetic energy evaluated in certain characteristic volumes, and in all of space, is identical in the two cases. Dirac's suggestion in 1962 of a bubble‐surface representing the electron is applied in a far‐reaching, but incomplete, attempt to identify external kinetic energy with a first‐order relativistic effect and the internal energy constituting the difference between Schrödinger and Ruedenberg's proposals is related to oscillations of the surface.

Heinz Otto Cordes

Emil Blomquist, Trotte Boman

The Dirac equation is a relativistic wave equation and was the first equation to capture spin in relativistic quantum mechanics. Here, the Dirac equation will be derived and solved for a particle in a spherical box potential. Comparisons to the non-relativistic Schrödinger equation as well as to a relativistically corrected Schrödinger equation will be made. Applications of the Dirac equation, such as the Bogoliubov model, are examined and discussed and it is validated that the Dirac equation can provide knowledge about elementary particles.

Xiaozheng Ma, Costas M. Soukoulis

Spyros Efthimiades

The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total kinetic plus potential energies. We derive the Schrodinger and Dirac equations as the unique conditions the wavefunction must satisfy at each point in order to fulfill the corresponding energy equation. PACS numbers: 03.65.-w. Keywords: Schrodinger equation; Dirac equation; Quantum dynamics.