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The angular momentum of m is proportional to the perpendicular component v ⊥ of the velocity, or equivalently, to the perpendicular distance r ⊥ from the origin. Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity (in radians/sec) about a ...
The term "azimuthal quantum number" was introduced by Arnold Sommerfeld in 1915 [1]: II:132 as part of an ad hoc description of the energy structure of atomic spectra. . Only later with the quantum model of the atom was it understood that this number, ℓ, arises from quantization of orbital angular moment
The classical definition of angular momentum is =.The quantum-mechanical counterparts of these objects share the same relationship: = where r is the quantum position operator, p is the quantum momentum operator, × is cross product, and L is the orbital angular momentum operator.
In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi-electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity .
In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number ( m l or m [ a ] ) distinguishes the orbitals available within a given subshell of an atom.
A particular application of the ladder operator concept is found in the quantum-mechanical treatment of angular momentum. For a general angular momentum vector J with components J x, J y and J z one defines the two ladder operators [3] + = +, =, where i is the imaginary unit.
The Bohr model gives an incorrect value L=ħ for the ground state orbital angular momentum: The angular momentum in the true ground state is known to be zero from experiment. Although mental pictures fail somewhat at these levels of scale, an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to revolve ...
In hyperfine structure, the total angular momentum of the atom is = + , where is the nuclear spin angular momentum and is the total angular momentum of the electron(s). Since F = I + J {\displaystyle ~F=I+J~} has a similar mathematical form as J = L + S , {\displaystyle ~J=L+S~,} it obeys a selection rule table similar to the table above.