Energy levels degenerate

The observed Schottky-specific heat is due to changes in internal energy that occur when nearly adjacent energy levels are occupied. The degenerate energy levels may be caused by external or internal magnetic fields. 

The partition function, defined in terms of (degenerate) energy levels, rather than states, is... 

The argument may be extended to degenerate energy levels. Suppose there are three distinct wave functions corresponding to particle I at energy... 

Note that, for the degenerate energy levels (3.142b) and (3.142c) or (3.142d) and (3.142e), any linear combination of the chosen 02 and 03 or 4 and 05 would be equally valid.)... 

This expression is for singly degenerate energy levels. For an initial state with degeneracy, expression must be multiplied by i/g. 

Exchange and Correlation in Density Functional Theory of Atoms and Molecules degenerate energy level... 

Some of Fock s terminology may be mysterious to the modern reader. In particular, degenerate energy levels are energy eigenvalues whose eigenspaces are reducible (i.e., not irreducible) representations. 

Electronic absorption spectra have been recorded for a large number of oxomolybdenum(IV) species but, in addition to d-d transitions, there is the possibility of two-electron excitations, charge transfer bands and splitting of degenerate energy levels due to low symmetry. These factors make it difficult to interpret or even to compare spectra.5... 

A 3x3 block corresponding to P 1 which will produce three non-degenerate energy levels (alff-type) with MOs formed from a metal s-orbital, a combination of ligand s-orbitals (y> ) and a combination of ligand u-type p-orbitals (y l ). 

They will both produce identical energy levels and identical values for the coefficients of the symmetry-adapted basis functions in the final MOs. Again, it is necessary to solve eqn (12-2.1) for only one of the blocks. Overall we will have three doubly-degenerate energy levels (6,-type). 

A 3x3 determinant corresponding to F 1 which will produce three non-degenerate energy levels (a -type) and a corresponding set of MOs formed from combinations of the 4s, 3d , and yA orbitals. 

Two equivalent 2x2 determinants corresponding to r 1, one mixing the Sd i and y ((1> orbitals and the other mixing the 3d, and tpK <(l) orbitals (see Fig. 12-4.2 for the matching). These will provide two doubly-degenerate energy levels of etff-type. 

Looking at the character tables for Gn, we see that the one-dimensional representations with complex characters are grouped in pairs, such that one set of characters is the complex conjugate of the other set, and each pair of one-dimensional representations is labeled E, indicating doubly degenerate energy levels. The reason for this practice is as follows. The... 

Show that the sum of the n first-order energy corrections for an rt-fold degenerate energy level equals the sum of the n matrix elements H u in (1.207). 

The spin-orbit does not interact for the A-term or E-term manifolds as these kets do not involve the angular momentum (in the cubic groups). Consequently all the g-limes degenerate energy levels within the model space possess zero matrix elements of the spin-orbit operator. 

Fig. 4.20 Cyclic systems with degenerate energy levels tend to undergo a geometric distortion to remove the degeneracy, a consequence of the Jahn-Teller theorem...

An important special case arises when a valence electron of the central atom is on a degenerate energy level. Breaking the symmetry by some displacement, not of the totally symmetrical type, may lift the degeneracy and lower the total energy. Although such displacement lowers the total en-... 

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