Computational chemists often attempt to solve the non-relativistic Schrödinger equation, with relativistic corrections added, although some progress has been made in solving the fully relativistic Dirac equation.

Both of these features ( and more ) are incorporated in the relativistic Dirac equation, with predictions that come still closer to experiment.

The first step in solving a quantum chemical problem is usually solving the Schrödinger equation ( or Dirac equation in relativistic quantum chemistry ) with the electronic molecular Hamiltonian.

Via the Dirac equation, Dirac spinors are required in the mathematical description of the quantum state of the relativistic electron.

The following year, Paul Dirac discovered the fully relativistic theory of electron spin by showing the connection between spinors and the Lorentz group.

Likewise using the 4 × 4 Dirac gamma matrices gives rise to the 4 component Dirac spinors used in 3 + 1 dimensional relativistic quantum field theory.

In particle physics, the Dirac equation is a relativistic wave equation formulated by British physicist Paul Dirac in 1928.

In the new frame, remembering that the rest mass is a relativistic scalar, the Dirac equation will then take the form

then we have the transformed Dirac equation in a way that demonstrates manifest relativistic invariance:

The entire Dirac spinor represents an irreducible whole, and the components we have just neglected to arrive at the Pauli theory will bring in new phenomena in the relativistic regime-antimatter and the idea of creation and annihilation of particles.

4 for a step-by-small-step introduction to the Dirac equation, spinors, and relativistic spin / helicity operators.

We also note that a two-body Dirac equation composed of a Dirac operator for each of the two point particles interacting via the Coulomb interaction can be exactly separated in the ( relativistic ) center of momentum frame and the resulting ground state eigenvalue has been obtained very accurately using the Finite element methods of J. Shertzer.

* 1928 Paul Dirac states his relativistic electron quantum wave equation

Due to relativistic effects ( Dirac equation ), there is a magnetic momentum, μ < sub > S </ sub >, arising from the electron spin

Although Richard Feynman noted that a simplistic interpretation of the relativistic Dirac equation runs into problems with electron orbitals at Z > 1 / α = 137, suggesting that neutral atoms cannot exist beyond untriseptium, and that a periodic table of elements based on electron orbitals therefore breaks down at this point, a more rigorous analysis calculates the limit to be Z ≈ 173, but also that this limit would not actually spell the end of the periodic table.

The relativistic Dirac equation has problems for Z > 137, for the ground state energy is

In quantum theory the invariant mass is a parameter in the relativistic Dirac equation for an elementary particle.

Paul Dirac, for example, used algebraic constructions to produce a relativistic model for the electron, predicting its magnetic moment and the existence of its antiparticle, the positron.

* The Gaussian coherent states of nonrelativistic quantum mechanics can be generalized to relativistic coherent states of Klein-Gordon and Dirac particles.

As of November 2008, Dirac video playback is supported by VLC media player ( version 0. 9. 2 or newer ), and by applications using the GStreamer framework ( such as Songbird, Rhythmbox and Totem ).

In 1930, Paul Dirac developed a new version of the Wave Equation which was relativistically invariant ( unlike Schrödinger's one ), and predicted the magnetic moment correctly, and at the same time treated the electron as a point particle.

Scientists who accepted his invitation include luminaries such as Paul Dirac, Erwin Schrödinger, Werner Heisenberg, Hendrik Lorentz and Niels Bohr.

The situation changed rapidly in the years 1925 – 1930, when working mathematical foundations were found through the groundbreaking work of Erwin Schrödinger, Werner Heisenberg, Max Born, Pascual Jordan, and the foundational work of John von Neumann, Hermann Weyl and Paul Dirac, and it became possible to unify several different approaches in terms of a fresh set of ideas.

Although Schrödinger himself after a year proved the equivalence of his wave-mechanics and Heisenberg's matrix mechanics, the reconciliation of the two approaches and their modern abstraction as motions in Hilbert space is generally attributed to Paul Dirac, who wrote a lucid account in his 1930 classic Principles of Quantum Mechanics.

File: Dirac 4. jpg | Paul Dirac ( 1902-1984 ): made fundamental contributions to the early development of quantum mechanics and quantum electrodynamics, formulated the Dirac equation describing the behavior of fermions, predicted the existence of antimatter, shared the1933 Nobel Prize in Physics with Erwin Schrödinger,

The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld and others.

One of the oldest and most commonly used formulations is the " transformation theory " proposed by the late Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics-matrix mechanics ( invented by Werner Heisenberg ) and wave mechanics ( invented by Erwin Schrödinger ).

Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein-Gordon equation or the Dirac equation.

Attempted replacements for the Schrödinger equation, such as the Klein-Gordon equation or the Dirac equation, have many unsatisfactory qualities ; for instance, they possess energy eigenvalues that extend to –∞, so that there seems to be no easy definition of a ground state.

* Physics – Erwin Schrödinger, Paul Adrien Maurice Dirac

In 1925 and 1927, Mulliken traveled to Europe, working with outstanding spectroscopists and quantum theorists such as Erwin Schrödinger, Paul A. M. Dirac, Werner Heisenberg, Louis de Broglie, Max Born, and Walther Bothe ( all of whom eventually received Nobel Prizes ) and Friedrich Hund, who was at the time Born's assistant.

Up until that time, attempts to make the old quantum theory of the atom compatible with the theory of relativity, attempts based on discretizing the angular momentum stored in the electron's possibly non-circular orbit of the atomic nucleus, had failed-and the new quantum mechanics of Heisenberg, Pauli, Jordan, Schrödinger, and Dirac himself had not developed sufficiently to treat this problem.

The Dirac equation is superficially similar to the Schrödinger equation for a free massive particle:

Thus the Schrödinger equation may be seen as the far non-relativistic approximation of the Dirac equation when one may neglect spin and work only at low energies and velocities.

* Schrödinger and dirac-research: implementations of the Dirac compression format developed by BBC Research at the BBC.

Heisenberg, de Broglie, Dirac, Bohr, Jeans, Weyl, Compton, Thomson, Schrödinger, Jordan, Millikan, Lemaître, Reichenbach, et al.

Those who used the techniques of calculus included Louis de Broglie, Erwin Schrödinger, Paul Dirac, Hermann Weyl, Oskar Klein, Walter Gordon, Douglas Hartree and Vladimir Fock.

A DirectShow filter exists for both Dirac and Schrödinger, although this is not supported on versions of Windows prior to Windows

This was, at first, followed by a heuristic framework devised by Arnold Sommerfeld and Niels Bohr, but this was soon replaced by the quantum mechanics developed by Max Born, Werner Heisenberg, Paul Dirac, Erwin Schrödinger, and Wolfgang Pauli.

Despite this usage of " covariant ", it is more accurate to say that the Klein – Gordon and Dirac equations are invariant, and that the Schrödinger equation is not invariant.

The origins of the Dirac sea lie in the energy spectrum of the Dirac equation, an extension of the Schrödinger equation that is consistent with special relativity, that Dirac had formulated in 1928.