Search results
Results from the WOW.Com Content Network
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.
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. Being an observable, its eigenfunctions represent the ...
The azimuthal quantum number, also known as the orbital angular momentum quantum number, describes the subshell, and gives the magnitude of the orbital angular momentum through the relation L 2 = ℏ 2 ℓ ( ℓ + 1 ) . {\displaystyle L^{2}=\hbar ^{2}\ell (\ell +1).}
To solve from the Schrödinger equation: varies with situation and number of particles Wavefunction probability density: ... j = total angular momentum quantum number;
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.
Here L is the total orbital angular momentum quantum number. [18] For atoms with a well-defined S, the multiplicity of a state is defined as 2 S + 1. This is equal to the number of different possible values of the total (orbital plus spin) angular momentum J for a given (L, S) combination, provided that S ≤ L (the typical case).
The spin magnetic quantum number m s specifies the z-axis component of the spin angular momentum for a particle having spin quantum number s. For an electron, s is 1 ⁄ 2 , and m s is either + 1 ⁄ 2 or − 1 ⁄ 2 , often called "spin-up" and "spin-down", or α and β.
The associated quantum number is the main total angular momentum quantum number j. It can take the following range of values, jumping only in integer steps: [ 1 ] | ℓ − s | ≤ j ≤ ℓ + s {\displaystyle \vert \ell -s\vert \leq j\leq \ell +s} where ℓ is the azimuthal quantum number (parameterizing the orbital angular momentum) and s is ...