Orbital Angular Momentum (other)

	Orbital Angular Momentum (other) Orbital angular momentum may refer to: * One of three main quantum angular momentum operators * Orbital angular momentum of light, a property of electromagnetic waves * Orbital angular momentum of free electrons, a property of free electrons * Orbital angular momentum of planets and satellites relative to the object they orbit {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Angular Momentum Operator In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Such an operator is applied to a mathematical representation of the physical state of a system and yields an angular momentum value if the state has a definite value for it. In both classical and quantum mechanical systems, angular momentum (together with linear momentum and energy) is one of the three fundamental properties of motion.Introductory Quantum Mechanics, Richard L. Liboff, 2nd Edition, There are several angular momentum operators: total angular momentum (usually denoted J), orbital angular momentum (usually denoted L), and spin angular momentum (spin for short, usually denoted S). The term ''angular momentum operator'' can (confusingly) refer to either the total or the orbital angular momen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Orbital Angular Momentum Of Light The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. It can be further split into an internal and an external OAM. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront. The external OAM is the origin-dependent angular momentum that can be obtained as cross product of the light beam position (center of the beam) and its total linear momentum. Introduction A beam of light carries a linear momentum \mathbf, and hence it can be also attributed an external angular momentum \mathbf_e=\mathbf\times\mathbf. This external angular momentum depends on the choice of the origin of the coordinate system. If one chooses the origin at the beam axis and the beam is cylindrically symmetric (at least in its momentum distribution), the external angular momentum will vanish. The external angul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Orbital Angular Momentum Of Free Electrons Electrons in free space can carry quantized orbital angular momentum (OAM) projected along the direction of propagation. This orbital angular momentum corresponds to helical wavefronts, or, equivalently, a phase proportional to the azimuthal angle. Electron beams with quantized orbital angular momentum are also called electron vortex beams. Theory An electron in free space travelling at non- relativistic speeds, follows the Schrödinger equation for a free particle, that is i\hbar\frac \Psi(\mathbf,t) = \frac\nabla^2 \Psi(\mathbf,t), where \hbar is the reduced Planck constant, \Psi(\mathbf r , t) is the single-electron wave function, m its mass, \mathbf r the position vector, and t is time. This equation is a type of wave equation and when written in the Cartesian coordinate system (x,y,z), the solutions are given by a linear combination of plane waves, in the form of \Psi_(\mathbf,t)\propto e^ where \mathbf is the linear momentum and E(\mathbf) is the electron energy, given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]