Degeneracy of a level

L, S, and / are required to describe the electronic state. Placing the ion in a crystal field affects the energy levels in two ways. First, the levels are shifted to the extent that they are repulsed by the field. Secondly, the field makes it possible to remove some of the degeneracy of a / level the crystal field splitting into the Mj components is in the order of 30—300 cm". ... 

The semiconductor surface where the Fermi level is pinned at a surface state of high density (Fig. 2-31) is in the state of degeneracy of electron levels, because of the high electron state density at the surface Fermi level. Similarly, the surface degeneracy is also established when the band bending becomes so great that the Fermi level is pinned either in the conduction band or in the valence band as shown in Fig. 2-32. 

Fia. 24. Energy level diagram for 3d configuraUon quartet terms under the action of crystal fields of various symmetries. Orbital degeneracy of a state is indicated in parentheses. 

Loss of degeneracy of energy levels of molecular entities due to lower site symmetry created by a crystalhne environment this term is not synonymous with hgand field splitting. See Ligand Field Splitting Comm, on Photochem. (1988), Pure and Appl. Chem. 60, 1055. 

The most important fact about m is that for a given l, it can take 21 + 1 possible values according to eqn 3.56 this therefore gives the degeneracy of the levels. 

A study of the spin-allowed bands in this complex has revealed that there is no observable phase-coupling effect [50]. According to Atanasov et al. [50] this must be explained by the near-degeneracy of donor levels of tft and % symmetry type. We consider it also conceivable that coordination of the metal ion polarizes the charge distribution in the ligand chain as depicted below ... 

Harris and Bertolucci [16] illustrated the relationship between symmetry and degeneracy of energy levels with a simple and attractive example. There are three parrallelepipeds in Figure 6-2. Each of them has six stable resting positions. The potential energy of these positions depends on the height of the center of the mass above the... 

The number of terms that have to be considered in this series depends on the symmetry. The ligand field perturbation lifts the 27 + 1 degeneracy of a particular 7 level and the eigen values of the operator Jz are required to label the states. 

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