Why Do Bound States Exhibit Flat Dispersions in Spectroscopy?

[fk08]

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

 

[olgranpappy]

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.