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e. In quantum mechanics, the Pauli equation or Schrödinger–Pauli equation is the formulation of the Schrödinger equation for spin-1/2 particles, which takes into account the interaction of the particle's spin with an external electromagnetic field. It is the non- relativistic limit of the Dirac equation and can be used where particles are ...
For n = 0, the equations reduce to the coupled Dirac equations and A and B together transform as the original Dirac spinor. Eliminating either A or B shows that A and B each fulfill . [2] The direct derivation of the Dirac-Pauli-Fierz equations using the Bargmann-Wigner operators is given in. [6]
The Schrödinger equation is a linear differential equation, meaning that if two state vectors and are solutions, then so is any linear combination of the two state vectors where a and b are any complex numbers. [13]: 25 Moreover, the sum can be extended for any number of state vectors.
In the non-relativistic limit the Dirac equation reduces to the Pauli equation (see Dirac equation for how). When applied a one-electron atom or ion, setting A = 0 and ϕ to the appropriate electrostatic potential, additional relativistic terms include the spin–orbit interaction, electron gyromagnetic ratio, and Darwin term.
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model 's electron orbits.
v. t. e. In quantum mechanics, the probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability. Specifically, if one thinks of probability as a heterogeneous fluid, then the probability current is the rate of flow of this fluid. It is a real vector that changes with space and time.
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later ...
v. t. e. The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, stemming from the work of Niels Bohr, Werner Heisenberg, Max Born, and others. [1] While "Copenhagen" refers to the Danish city, the use as an "interpretation" was apparently coined by Heisenberg during the 1950s to refer to ideas developed ...