tom.stoer said:In non-rel. QM one starts with the same 1/r potential. What else do you have in mind?
Choose a gauge in which the vector potential A = 0, leaving just the Coulomb 1/r potential. Separate variables in spherical coordinates as usual, and you'll find that the four components of the Dirac spinor can be written in terms of two radial functions, leding to recursion relations, etc, etc, and solved by confluent hypergeometric functions.I was just wondering that since the time-independent part of the solution is in vector form you might have to consider a potential in the form of a vector field. But maybe i´m wrong?
Bill_K said:Choose a gauge in which the vector potential A = 0, leaving just the Coulomb 1/r potential. Separate variables in spherical coordinates as usual, and you'll find that the four components of the Dirac spinor can be written in terms of two radial functions, leding to recursion relations, etc, etc, and solved by confluent hypergeometric functions.
The Dirac equation of the hydrogen atom is a relativistic quantum mechanical equation that describes the behavior of an electron in the hydrogen atom. It was developed by physicist Paul Dirac in 1928 and combines principles of special relativity and quantum mechanics.
The Schrödinger equation, developed in 1926, describes the behavior of non-relativistic particles, while the Dirac equation takes into account relativistic effects. The Dirac equation also predicts the spin of the electron, which the Schrödinger equation does not.
The Dirac equation is significant because it accurately describes the energy levels and wave functions of the hydrogen atom, which were previously only approximated by the Bohr model. It also provides a more complete understanding of the behavior of electrons in atoms.
The Dirac equation is solved using a set of mathematical techniques called perturbation theory. This involves making small adjustments to the known solutions of the Schrödinger equation for the hydrogen atom to account for the relativistic effects described by the Dirac equation.
While the Dirac equation accurately describes the behavior of the hydrogen atom, it does not fully account for the effects of quantum electrodynamics, which is necessary for understanding the behavior of particles at high energy levels. Additionally, it does not account for the presence of other particles in the atom, such as protons and neutrons.