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In quantum mechanics, the Pauli equation or Schrödinger–Pauli equation is the formulation of the Schrödinger equation for spin-½ 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 moving at speeds much less than the speed of light, so that relativistic effects can be neglected. It was formulated by Wolfgang Pauli in 1927.〔Wolfgang Pauli (1927) ''Zur Quantenmechanik des magnetischen Elektrons'' ''Zeitschrift für Physik'' (43) 601-623〕 == Equation == For a particle of mass ''m'' and charge ''q'', in an electromagnetic field described by the vector potential A = (''Ax'', ''Ay'', ''Az'') and scalar electric potential ''ϕ'', the Pauli equation reads: where σ = (''σx'', ''σy'', ''σz'') are the Pauli matrices collected into a vector for convenience, p = −''iħ''∇ is the momentum operator wherein ∇ denotes the gradient operator, and : is the two-component spinor wavefunction, a column vector written in Dirac notation. The Hamiltonian operator : is a 2 × 2 matrix operator, because of the Pauli matrices. Substitution into the Schrödinger equation gives the Pauli equation. This Hamiltonian is similar to the classical Hamiltonian for a charged particle interacting with an electromagnetic field, see Lorentz force for details of this classical case. The kinetic energy term for a free particle in the absence of an electromagnetic field is just p2/2''m'' where p is the ''kinetic'' momentum, while in the presence of an EM field we have the minimal coupling p = P − qA, where P is the canonical momentum. The Pauli matrices can be removed from the kinetic energy term, using the Pauli vector identity: : to obtain where B = ∇ × A is the magnetic field. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pauli equation」の詳細全文を読む スポンサード リンク
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