The problem was resolved by Dirac in the late 1920s, when he furthered the application of equation ( 2) to the electron – by various manipulations he factorized the equation into the form:Īnd one of these factors is the Dirac equation (see below), upon inserting the energy and momentum operators. Weyl found a relativistic equation in terms of the Pauli matrices the Weyl equation, for massless spin- 1 / 2 fermions.
The first two-dimensional spin matrices (better known as the Pauli matrices) were introduced by Pauli in the Pauli equation the Schrödinger equation with a non-relativistic Hamiltonian including an extra term for particles in magnetic fields, but this was phenomenological. The mysterious underlying property was spin. Neither the non-relativistic nor relativistic equations found by Schrödinger could predict the fine structure in the Hydrogen spectral series. Nevertheless, – ( 1) is applicable to spin-0 bosons. This equation was initially proposed by Schrödinger, and he discarded it for such reasons, only to realize a few months later that its non-relativistic limit (what is now called the Schrödinger equation) was still of importance. The KG equation is undesirable due to its prediction of negative energies and probabilities, as a result of the quadratic nature of ( 2) – inevitable in a relativistic theory. special relativity applied with quantum mechanics together, was found by all those who discovered what is frequently called the Klein–Gordon equation: The first basis for relativistic quantum mechanics, i.e. Late 1920s: Relativistic quantum mechanics of spin-0 and spin- 1 / 2 particles Ī description of quantum mechanical systems which could account for relativistic effects was sought for by many theoretical physicists from the late 1920s to the mid-1940s. At this point, special relativity was not fully combined with quantum mechanics, so the Schrödinger and Heisenberg formulations, as originally proposed, could not be used in situations where the particles travel near the speed of light, or when the number of each type of particle changes (this happens in real particle interactions the numerous forms of particle decays, annihilation, matter creation, pair production, and so on). The Schrödinger equation and the Heisenberg picture resemble the classical equations of motion in the limit of large quantum numbers and as the reduced Planck constant ħ, the quantum of action, tends to zero. The mathematical formulation was led by De Broglie, Bohr, Schrödinger, Pauli, and Heisenberg, and others, around the mid-1920s, and at that time was analogous to that of classical mechanics. The failure of classical mechanics applied to molecular, atomic, and nuclear systems and smaller induced the need for a new mechanics: quantum mechanics. History Early 1920s: Classical and quantum mechanics 3.2 Representations of the Lorentz group.3.1 Using 4-vectors and the energy–momentum relation.1.3 1930s–1960s: Relativistic quantum mechanics of higher-spin particles.
1.2 Late 1920s: Relativistic quantum mechanics of spin-0 and spin- 1 / 2 particles.1.1 Early 1920s: Classical and quantum mechanics.More generally – the modern formalism behind relativistic wave equations is Lorentz group theory, wherein the spin of the particle has a correspondence with the representations of the Lorentz group. Alternatively, Feynman's path integral formulation uses a Lagrangian rather than a Hamiltonian operator. All relativistic wave equations can be constructed by specifying various forms of the Hamiltonian operator Ĥ describing the quantum system.
One of the postulates of quantum mechanics. In the Schrödinger picture, the wave function or field is the solution to the Schrödinger equation The equations themselves are called "wave equations" or "field equations", because they have the mathematical form of a wave equation or are generated from a Lagrangian density and the field-theoretic Euler–Lagrange equations (see classical field theory for background).
The solutions to the equations, universally denoted as ψ or Ψ ( Greek psi), are referred to as " wave functions" in the context of RQM, and " fields" in the context of QFT. In the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields. In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light.
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