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An electron's angular momentum, L, is related to its quantum number ℓ by the following equation: = (+), where ħ is the reduced Planck constant, L is the orbital angular momentum operator and is the wavefunction of the electron.
Electrons in free space can carry quantized orbital angular momentum (OAM) projected along the direction of propagation. [1] This orbital angular momentum corresponds to helical wavefronts, or, equivalently, a phase proportional to the azimuthal angle. [2] Electron beams with quantized orbital angular momentum are also called electron vortex beams.
If the electron is visualized as a classical rigid body in which the mass and charge have identical distribution and motion that is rotating about an axis with angular momentum L, its magnetic dipole moment μ is given by: =, where m e is the electron rest mass. The angular momentum L in this equation may be the spin angular momentum, the ...
Quantum orbital motion involves the quantum mechanical motion of rigid particles (such as electrons) about some other mass, or about themselves.In classical mechanics, an object's orbital motion is characterized by its orbital angular momentum (the angular momentum about the axis of rotation) and spin angular momentum, which is the object's angular momentum about its own center of mass.
, the magnitude of the angular momentum in the -direction, is given by the formula: [7] L z = m l ℏ {\displaystyle L_{z}=m_{l}\hbar } . This is a component of the atomic electron's total orbital angular momentum L {\displaystyle \mathbf {L} } , whose magnitude is related to the azimuthal quantum number of its subshell ℓ {\displaystyle \ell ...
Each orbital in an atom is characterized by a set of values of three quantum numbers n, ℓ, and m ℓ, which respectively correspond to electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis (magnetic quantum number). The orbitals with a well-defined magnetic quantum number are generally ...
This would ultimately become the quantized values of the projection of spin, an intrinsic angular momentum quantum of the electron. In 1927 Ronald Fraser demonstrated that the quantization in the Stern-Gerlach experiment was due to the magnetic moment associated with the electron spin rather than its orbital angular momentum. [7]
The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.