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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 ...
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.
The total angular momentum of a particle is the sum of both its orbital angular momentum and spin angular momentum. [3] A particle's spin is generally represented in terms of spin operators. It turns out for particles that make up ordinary matter (protons, neutrons, electrons, quarks, etc.) particles are of spin 1/2. [4]
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]
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 ...
In molecules the total angular momentum F is the sum of the rovibronic (orbital) angular momentum N, the electron spin angular momentum S, and the nuclear spin angular momentum I. For electronic singlet states the rovibronic angular momentum is denoted J rather than N.
The orbital angular momentum of electrons is quantized. Because the electron is charged, it produces an orbital magnetic moment that is proportional to the angular momentum. The net magnetic moment of an atom is equal to the vector sum of orbital and spin magnetic moments of all electrons and the nucleus.