Understanding tight binding model

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SUMMARY

The discussion focuses on the tight binding model as illustrated in Figure 10.6 on page 184 of "Solid State Physics" by Ashcroft and Mermin. It clarifies that the line along the gamma point (Γ) is not doubly degenerate, while the line along the L point is doubly degenerate due to the energy values of d orbitals. The diagram indicates that there should be five lines representing the d orbital states, but only three and four are shown in the first two diagrams due to degeneracy effects, which result from overlapping solutions.

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mkbh_10
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Explain to me the Fig 10.6 given on page 184 in Ashcroft and Mermin.
How is line along gamma k not doubly degenerate and line along gamma L doubly degenerate ?
 
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Ashcroft is a bit long on text and short on pictures. What the diagram means is that it is actually showing the Energy values for a d orbital which should give 5 lines. Notice that in the first 2 diagrams there are only 3 and 4 each because of degeneracy. In other words, the solutions overlap
 

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