Pauliyhtälö

Pauliyhtälö, often translated as Pauli equation, is a fundamental equation in quantum mechanics that describes the behavior of a non-relativistic particle with spin-1/2 in an external electromagnetic field. It is a relativistic generalization of the Schrödinger equation and is named after the Austrian physicist Wolfgang Pauli.

The equation incorporates the effects of spin, a fundamental intrinsic angular momentum of particles. It is formulated using the Pauli matrices, which represent spin operators. The presence of an external magnetic field is accounted for by the inclusion of the vector potential and scalar potential in the Hamiltonian.

The Pauli equation is crucial for understanding phenomena such as the Zeeman effect, where spectral lines split in the presence of a magnetic field due to the interaction of the electron's spin magnetic moment with the field. It also forms the basis for describing the behavior of electrons in atoms and molecules, and plays a role in solid-state physics. While it is a non-relativistic approximation, it provides accurate results for many physical systems where particle velocities are significantly less than the speed of light. The Dirac equation, a fully relativistic quantum mechanical equation, is a more complete description that includes spin and relativistic effects but is more complex.