Spin quantum numberIn physics, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = 1/2 for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons. The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written ms.
Pauli matricesIn mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted by tau (τ) when used in connection with isospin symmetries. These matrices are named after the physicist Wolfgang Pauli. In quantum mechanics, they occur in the Pauli equation which takes into account the interaction of the spin of a particle with an external electromagnetic field.
SpinorIn geometry and physics, spinors spɪnɚ are elements of a complex number-based vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation, but unlike geometric vectors and tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to its original state.
Wave functionIn quantum physics, a wave function (or wavefunction), represented by the Greek letter Ψ, is a mathematical description of the quantum state of an isolated quantum system. In the Copenhagen interpretation of quantum mechanics, the wave function is a complex-valued probability amplitude; the probabilities for the possible results of the measurements made on a measured system can be derived from the wave function. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively).
Schrödinger equationThe Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. The equation is named after Erwin Schrödinger, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics.
Spin-1/2In quantum mechanics, spin is an intrinsic property of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of 1/2. The spin number describes how many symmetrical facets a particle has in one full rotation; a spin of 1/2 means that the particle must be rotated by two full turns (through 720°) before it has the same configuration as when it started. Particles having net spin 1/2 include the proton, neutron, electron, neutrino, and quarks.
