Quantum molecular dynamics

Abstract

Electron or ion dynamics are treated using spin-dependent quantum trajectories. These trajectories are inferred from the Dirac current, which contributes Schroedinger's current and additional spin-dependent terms, all of which are of order c 0 in the nonrelativistic regime of particle velocity, where c is the speed of light. The many-body problem is treated precisely as in classical dynamics. Each electron or ion has its own equation of motion, which is the time-dependent Dirac or the timedependent Schroedinger equation in the relativistic or nonrelativistic regime of particle velocity, respectively. As an example the theory is applied to the electronic structure of the helium atom, in which two electrons with opposite spin states are shown to correlate such that their quantum trajectories keep them on average on opposite sides of the nucleus. As the theory is time dependent, excited states are also generated.

Quantum-Dynamical Theory of Electron Exchange Correlation

“…(Preliminary He-atom calculations were presented previously [12].) The computational grid box is square with a uniform mesh of 32 3 .…”

“…The positions of the spectral peaks ( Figure 3) are accurately predicted even for early times and wide spectral lines, as measured by Δ , but the integration should be continued for long enough times that the spectral peaks for different eigenvalues are well separated. This may be hard to accomplish for integrating (12) for heavy particles. Figure 1 shows quantum trajectories in the y direction for up and down spin states and identical spatial orbitals at initial time.…”

Electromagnetic-wave Contribution to the Quantum Structure of Matter

“…where we have used the identity, ( [8], which is a spin-dependent phenomenon. The history of quantum mechanics instead followed a path of ensuring that Schroedinger wave functions satisfy Fermi-Dirac statistics on the basis of experimental observation and not a priori theory by using the Slater determinantal wave function to solve Schroedinger's wave equation for many electrons, even though Schroedinger theory, in which particle spin is absent, contains no physical basis for FermiDirac statistics.…”

“…The history of quantum mechanics instead followed a path of ensuring that Schroedinger wave functions satisfy Fermi-Dirac statistics on the basis of experimental observation and not a priori theory by using the Slater determinantal wave function to solve Schroedinger's wave equation for many electrons, even though Schroedinger theory, in which particle spin is absent, contains no physical basis for FermiDirac statistics. One must instead turn to time-domain Dirac theory and the Dirac current to discover the physical basis for Fermi-Dirac statistics, which is elucidated using spindependent quantum trajectories [8]. Richard Feynman [9] once asked if spin is a relativistic requirement and then answered in the negative because the Klein-Gordon equation is a valid relativistic equation for a spin-0 particle.…”

General solution of the coulomb–dirac problem: calculation of a divergence‐free lamb shift

“…Clearly Dirac's use of the Schroedinger forms wðr; tÞ ¼ e Ài E h t w E ðrÞ and vðr; tÞ ¼ e Ài E h t v E ðrÞ to write the energy domain form of his coupled time-dependent equations [Eqs. (8)] rests on an implicit assumption that adiabatic elimination of one of these equations in favor of the other is an accurate approximation. On other words, the Schroedinger form does not hold exactly in the case of a vector wave function whose components are temporally coupled.…”