L, orbital angular momentum

L orbital angular momentum vector operator (of a cation)... 

L orbital angular momentum X bulk magnetic susceptibility... 

DCD DC demagnetizing remanence magnetization L orbital angular momentum... 

L = orbital angular momentum quantum r = crystal field level ... 

When the molecule is not in a S state there is an interaction between the rotation of the molecule and S and/or L, and the details of coupling the angular momenta are involved. Most nonsinglet molecules with electronic orbital angular momentum A = 0 obey Hund s case (b) coupling. In Case (b), the electronic orbital angular momentum combines with the nuclear orbital angular... 

For all produet states of this Ms value, one identifies the highest Ml value (this gives a value of the total orbital angular momentum, L, that ean arise for this S). For the above example, the highest Ml within the Ms =1 states is Ml = 1 (not Ml = 2), henee L=1. 

The above m funetions are appropriate whenever one wishes to deseribe orbitals that are eigenfunetions of L, the eomponent of orbital angular momentum along the z-axis. 

A particle moving with momentum p at a position r relative to some coordinate origin has so-called orbital angular momentum equal to L = r x p. The three components of this angular momentum vector in a cartesian coordinate system located at the origin mentioned above are given in terms of the cartesian coordinates of r and p as follows ... 

The functions are known as the angular wave functions or, because they describe the distribution of p over the surface of a sphere of radius r, spherical harmonics. The quantum number n = l,2,3,...,oo and is the same as in the Bohr theory, is the azimuthal quantum number associated with the discrete orbital angular momentum values, and is... 

Flowever, the values of the total orbital angular momentum quantum number, L, are limited or, in other words, the relative orientations of f j and 2 are limited. The orientations which they can take up are governed by the values that the quantum number L can take. L is associated with the total orbital angular momentum for the two electrons and is restricted to the values... 

It can be shown quite easily that, for a filled sub-shell such as 2p or L = 0. Space quantization of the total orbital angular momentum produces 2L - - 1 components with M] = L, L —, —L, analogous to space quantization of f. In a filled sub-shell... 

Previously we have considered the promotion of only one electron, for which Af = 1 applies, but the general mle given here involves the total orbital angular momentum quantum number L and applies to the promotion of any number of electrons. 

The vector L is so strongly coupled to the electrostatic field and the consequent frequency of precession about the intemuclear axis is so high that the magnitude of L is not defined in other words L is not a good quantum number. Only the component H of the orbital angular momentum along the intemuclear axis is defined, where the quantum number A can take the values... 

Any operator J, which satisfies the commutation rule Eq. (7-18), represents quantum mechanical angular momentum. Orbital angular momentum, L, with components explicitly given by Eq. (7-1), is a special example5 of J. 

For a spinless particle the total angular momentum, J, is equal to L, the orbital angular momentum. It may, however, be the case that the total angular momentum is not equal to Z1 as given by (9-52), but is of the form... 

The elements of S-matrices are determined in the basis of orbital angular momentum l and rotational moments jt,jf of vibrational states i,f and their projections (m,m,-,m/). Both S-matrices in Eq. (4.58) have to be calculated for the same energy Ek of colliding particles. 

Here L, S, and J are the quantum numbers corresponding to the total orbital angular momentum of the electrons, the total spin angular momentum, and the resultant of these two. Hund predicted values of L, S, and J for the normal states of the rare-earth ions from spectroscopic rules, and calculated -values for them which are in generally excellent agreement with the experimental data for both aqueous solutions and solid salts.39 In case that the interaction between L and S is small, so that the multiplet separation corresponding to various values of J is small compared with kT, Van Vleck s formula38... 

A term label like for example, is thus no longer strictly meaningful for it implies constant spin- and orbital angular momentum properties (5 = 1, L = 3). One consequence of spin-orbit coupling is a scrambling of the two kinds of angular momentum. So a nominal term may really more properly be described as a mixture of terms of different spin-multiplicity as, for example, in Eq. (4.10). 

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