Point of equal energy

Figure 4.7 Gamut of colors in CIE XYZ space. The chromaticities of light in the visible range from 400 nm to 700 nm form a horseshoe-shaped region. The chromaticities for a black-body radiator at different temperatures is shown in the center. The color of a black-body radiator passes from red at low temperatures through white and on to blue at higher temperatures. The point of equal energy is located at the center of the graph.

Earlier in this chapter we considered the effect of orbital interactions on a previously noninteracting system. But suppose now we take as starting point two interacting orbitals 4>A and B of equal energy and we introduce a change in electronegativity at centers A and B. The qualitative results of such a perturbation are again well known from elementary quantum chemistry ... 

To improve our model still further, we have to visualize s- and p-orbitals as waves of electron density centered on the nucleus of an atom. Like waves in water, the four orbitals interfere with one another and produce new patterns where they intersect. These new patterns are called hybrid orbitals. The four hybrid orbitals are identical to one another except that they point toward different comers of a tetrahedron (Fig. 3.16). Each orbital has a node close to the nucleus and a small tail on the other side where the s- and p-orbitals do not completely cancel. These four hybrid orbitals are called sp3 hybrids because they are formed from one s-orbital and three p-orbitals. In an orbital-energy diagram, we represent the hybridization as the formation of four orbitals of equal energy intermediate between the energies of the s- and /7-orbitals from which they are constructed (43). The hybrids are colored green to remind us that they are a blend of (blue) s-orbitals and (yellow) p-orbitals. 

When the unperturbed basis orbitals are of equal energy, each makes an equal contribution to the perturbed orbital. In other words, at each point the values... 

The Dirac equation is of the same order in all variables (space and time), since the momentum operator p (= — iV) involves a first-order differentiation with respect to the space variables. It should be noted that the free electron rest energy in eq. (8.3) is mc, equal to 0.511 MeV, while this situation is defined as zero in the non-relativistic case. The zero point of the energy scale is therefore shifted by 0.511 MeV, a large amount compared with the binding energy of 13.6eV for a hydrogen atom. The two energy... 

G-T plot, the intersection of curves generated for two different crystalline phases represents a point of equal free energy and a transition temperature. 

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