Degeneracy, definition

Notice that if and P2 contain different function or test letters then strong equivalence between and implies a kind of degeneracy, in that certain functions and predicates are not really needed. We need a different type definition of equivalence to handle the case in which different schemes compute the same function under varying interpretations of the functions they do not have in common. 

For degenerate states a problem arises with the definition of cumulants. We consider here only spin degeneracy. Spatial degeneracy can be discussed on similar lines. For S 0 there are (2S + 1) different Afs-values for one S. The n-particle density matrix p Ms) = of a single one of these states does not... 

The other degree of freedom in defining Vee related to the degeneracy of the 1-RDM can be avoided with a proper definition of the diagonal part (uee) (see Ref. [81]). As a consequence, the NOs with the same ON are determined only up to the unitary transformation among them. 

The parameter (v) is the average thermal velocity of an electron, Nc the density of states in the conduction band, g the degeneracy of the deep level, and A x = EQ — ET the electron transition energy. Equation (9) also relates the capture constant to the emission rate because of the definition... 

Spherical harmonics, 29, 38 Spherical polar coordinates, 21 Spherical top definition of, 199 degeneracy for, 210 degenerate vibrational modes in, 276 energies of, 209-210 microwave spectrum of, 217,225 polarizability, 202 wave functions of, 209, 211... 

Interaction of the momenta is contained in a non-spherical part of the Coulomb interaction and in the spin-orbit interaction. The value of the energy of the interaction of two momenta depends on the angle between them, therefore, in such a case the definite inter-orientation of all one-electronic momenta is settled. Differently oriented states have different energy, i.e. the zero-order level splits into sublevels and its degeneracy disappears. 

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