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In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light ''c'', and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. ''Non-relativistic quantum mechanics'' refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. ''Relativistic quantum mechanics'' (RQM) is quantum mechanics applied with special relativity, but not general relativity. An attempt to incorporate general relativity into quantum theory is the subject of quantum gravity, an unsolved problem in physics, although some theories, such as the Kaluza-Klein, have been proposed but are unfounded and without proof. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, these pictures of quantum mechanics also apply with special relativity. The relativistic formulation is more successful than the original quantum mechanics in some contexts, in particular: the prediction of antimatter, electron spin, spin magnetic moments of elementary spin-1/2 fermions, fine structure, and quantum dynamics of charged particles in electromagnetic fields. The key result is the Dirac equation, from which these predictions emerge automatically. By contrast, in quantum mechanics, terms have to be introduced artificially into the Hamiltonian operator to achieve agreement with experimental observations. Nevertheless, RQM is only an approximation to a fully self-consistent relativistic theory of known particle interactions because it does not describe cases where the number of particles changes; for example in matter creation and annihilation. By yet another theoretical advance, a more accurate theory that allows for these occurrences and other predictions is ''relativistic quantum field theory'' in which particles are interpreted as ''field quanta'' (see article for details). In this article, the equations are written in familiar 3d vector calculus notation and use hats for operators (not necessarily in the literature), and where space and time components can be collected, tensor index notation is shown also (frequently used in the literature), in addition the Einstein summation convention is used. SI units are used here; Gaussian units and natural units are common alternatives. All equations are in the position representation; for the momentum representation the equations have to be Fourier transformed – see position and momentum space. ==Combining special relativity and quantum mechanics== One approach is to modify the Schrödinger picture to be consistent with special relativity.〔 A postulate of quantum mechanics is that the time evolution of any quantum system is given by the Schrödinger equation: : using a suitable Hamiltonian operator corresponding to the system. The solution is a complex-valued wavefunction , a function of the 3d position vector of the particle at time , describing the behavior of the system. Every particle has a non-negative spin quantum number . The number is an integer, odd for fermions and even for bosons. Each has ''z''-projection quantum numbers; .〔Other common notations include and etc., but this would clutter expressions with unnecessary subscripts. The subscripts labeling spin values are not to be confused for tensor indices nor the Pauli matrices.〕 This is an additional discrete variable the wavefunction requires; . Historically, in the early 1920s Pauli, Kronig, Uhlenbeck and Goudsmit were the first to propose the concept of spin. The inclusion of spin in the wavefunction incorporates the Pauli exclusion principle (1925) and the more general spin-statistics theorem (1939) due to Fierz, rederived by Pauli a year later. This is the explanation for a diverse range of subatomic particle behavior and phenomena: from the electronic configurations of atoms, nuclei (and therefore all elements on the periodic table and their chemistry), to the quark configurations and color charge (hence the properties of baryons and mesons). A fundamental prediction of special relativity is the relativistic energy–momentum relation; for a particle of rest mass , and in a particular frame of reference with energy and 3-momentum with magnitude in terms of the dot product , it is: : These equations are used together with the energy and momentum operators, which are respectively: : This equation is also true in RQM, provided the Heisenberg operators are modified to be consistent with SR. Historically, around 1926, Schrödinger and Heisenberg show that wave mechanics and matrix mechanics are equivalent, later furthered by Dirac using transformation theory. A more modern approach to RWEs, first introduced during the time RWEs were developing for particles of any spin, is to apply representations of the Lorentz group. 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「Relativistic quantum mechanics」の詳細全文を読む スポンサード リンク
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