Why Do Bound States Exhibit Flat Dispersions in Spectroscopy?

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SUMMARY

Bound states in spectroscopy exhibit flat dispersions due to their tightly bound nature, as discussed in Ashcroft and Mermin. Unlike surface states and quantum well states, which display free-electron-like dispersions (E ≈ k*k), d-electrons are characterized by their flat dispersions resulting from the tight binding model. The overlap integral in this model is directly proportional to the bandwidth, indicating that more tightly bound atomic states lead to flatter bands.

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  • Tight binding model in solid-state physics
  • Understanding of dispersion relations in quantum mechanics
  • Familiarity with Ashcroft and Mermin's principles
  • Basic concepts of spectroscopy and electronic states
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  • Study the tight binding model and its implications on electronic band structure
  • Explore the relationship between overlap integrals and bandwidth in solid-state physics
  • Investigate the differences between free-electron and bound state dispersions
  • Review quantum mechanics principles related to Heisenberg's uncertainty principle
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Physicists, materials scientists, and students studying solid-state physics and spectroscopy, particularly those interested in electronic band structures and their implications in various materials.

fk08
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Hello,

i ve got some questions on spectroscopy. surface states and quantum well states have free-electron like dispersions, they a more or less free states, so E ≈ k*k. d-electrons have flat dispersions, they are bound. My Question is: why have bound states flat dispersions? does this have something to do with heissenberg? which means E*x ≈ constant ?
Thaks
 
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fk08 said:
Hello,

i ve got some questions on spectroscopy. surface states and quantum well states have free-electron like dispersions, they a more or less free states, so E ≈ k*k. d-electrons have flat dispersions, they are bound. My Question is: why have bound states flat dispersions? does this have something to do with heissenberg? which means E*x ≈ constant ?
Thaks

this is discussed in Ashcroft and Mermin. In the tight binding picture the overlap integral is proportional to the bandwidth so that more tightly bound atomic states give rise to flatter bands.
 

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