NOTICE: Citizendium is still being set up on its newer server, treat as a beta for now; please see here for more.
Citizendium - a community developing a quality comprehensive compendium of knowledge, online and free. Click here to join and contribute—free
CZ thanks our previous donors. Donate here. Treasurer's Financial Report -- Thanks to our content contributors. --

Orbital-angular momentum

From Citizendium, the Citizens' Compendium
(Redirected from Orbital angular momentum)
Jump to: navigation, search
This article is developing and not approved.
Main Article
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
This editable Main Article is under development and not meant to be cited; by editing it you can help to improve it towards a future approved, citable version. These unapproved articles are subject to a disclaimer.
See also angular momentum in quantum mechanics

In quantum mechanics, orbital angular momentum is a conserved property of a system of one or more particles that are in a centrally symmetric potential. If the radius of particle k with respect to the center of symmetry is rk = (xk, yk, zk) and if the momentum of the same particle is pk, then the orbital angular momentum of particle k is defined as the following vector operator,

where the symbol × indicates the cross product of two vectors. The total angular momentum of a system of N particles is

In the so-called x-representation of quantum mechanics, the vector rk is a multiplicative operator and

The components of the orbital angular momentum satisfy the following commutation relations,

The fact that L is a conserved quantity is expressed by the commutation with the Hamiltonian (energy operator)

It can be shown that this condition is necessary and sufficient that the potential energy part of H be centrally symmetric.