The Dirac Equation

Daehyeon Kang

Agualar momentum j in the Dirac equation and j in the schronger equation are eqaul or different ? they are equal. but, j=0 in the dirac equation is forbidden, j=0 in the schronger equation is allowed. from this fact, it seems Dirac equation is not appropriate to study atomic phenomenon. maybe, only in a central field of force.

Theodore Frankel

Yuri A. Rylov

Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute objects of the Dirac equation. There are two ways of the Dirac matrices transformation: (1) Dirac matrices form a 4-vector and wave function is a scalar, (2) Dirac matrices are scalars and the wave function is a spinor. In the first case the Dirac equation is nonrelativistic, in the second one it is relativistic. Transforming Dirac equation to another scalar-vector variables, one shows that the first way of transformation is valid, and the Dirac equation is not relativistic

Tom Lancaster, Stephen J. Blundell

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.