Degenerate systems

Wynne K and Hochstrasser R M 1995 Anisotropy as an ultrafast probe of electronic coherence in degenerate systems exhibiting Raman scattering, fluorescence, transient absorption and chemical reactions J. Raman Spectrosc. 26 561-9... 

This is the central Jahn-Teller [4,5] result. Three important riders should be noted. First, Fg = 0 for spin-degenerate systems, because F, x F = Fo. This is a particular example of the fact that Kramer s degeneracies, aiising from spin alone can only be broken by magnetic fields, in the presence of which H and T no longer commute. Second, a detailed study of the molecular point groups reveals that all degenerate nonlinear polyatomics, except those with Kramer s... 

Lowdin, P.-O., Phys. Rev. 97, 1474, 1490, 1509, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals and convergence problems in the method of configuration interaction. II. Study of the ordinary Hartree-Fock approximation. III. Extension of the Har-tree-Fock scheme to include degenerate systems and correlation effects. ... 

Spin-degenerate systems, geometric phase theory, conical intersections, 6-8 Spin function, permutational symmetry, group theoretical properties,... 

The Hamiltonian for two electrons in the field of two fixed protons is given by (39). For large values of rab the system reasonably corresponds to two H atoms. The wave functions of the degenerate system are ipi = ui5a(l)ui 6(2) and ip2 = UiSt(l)u1Sa(2), where ul5o(l) is the hydrogenic wave function for electron 1 about nucleus A, etc. For smaller values of rab a linear combination of the two product functions is a reasonable variational trial function, i.e. 1p = 1pl +... 

J. Gong and S. A. Rice. General method for complete population transfer in degenerate systems. Phys. Rev. A, 69(6) 063410-063418(2004). 

It was noted earlier that, in the absence of spin-orbit coupling, the spin part of the magnetic moment operator makes no contribution to MCD and spin degeneracy also plays no role in MCD spectroscopy. It was also noted that neglecting spin-orbit coupling led to qualitative errors in the predicted MCD spectra of some spin-degenerate systems. In this section we will present equations for the additional contributions to MCD that occur once spin-orbit coupling is included. 

For a degenerate system we cannot always determine beforehand the zero-order or model functions. The mixing of the degenerate eigenfunctions in the zero-order depends on the perturbation. Therefore, generally speaking, we can only confine the model function to a certain subspace of the entire functional space. Let us call this subspace the model (or P)... 

A source of this mistake is, in particular, the fact that one does not understand that for the solution of a degenerated system the formula... 

The initial system can be constructed as a series with respect to powers of [39], A zero approximation here is a solution of the degenerated system. This approach is, however, very rarely used since the increase of accuracy results in a significant complication of calculations. 

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