Questions on spectroscopy

In summary, the question is about the flat dispersions of bound states and whether this has something to do with Heisenberg, and the answer is that it is explained in Ashcroft and Mermin where it is stated that in the tight binding picture, the overlap integral is proportional to the bandwidth, resulting in flatter bands for more tightly bound atomic states.
  • #1
fk08
31
0
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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  • #2


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.
 
  • #3
for your questions on spectroscopy. The reason why bound states have flat dispersions is due to the quantum mechanical nature of electrons. In a bound state, the electron is confined to a specific region and has a limited range of motion. This confinement leads to a quantization of the electron's energy levels, resulting in discrete energy states rather than a continuous dispersion relationship. This is known as the Heisenberg Uncertainty Principle, which states that the position and momentum of a particle cannot be precisely known at the same time. This principle applies to electrons in bound states, leading to the flat dispersion relationship you mentioned. In contrast, free electrons have a wider range of motion and are not confined, allowing for a more continuous dispersion relationship. I hope this helps to answer your question.
 

1. What is spectroscopy?

Spectroscopy is a scientific technique used to study the interaction between matter and electromagnetic radiation. It involves the measurement and analysis of the different wavelengths of light that are absorbed, emitted, or scattered by a substance. This can provide information about the chemical composition, structure, and properties of the substance.

2. How is spectroscopy used in research?

Spectroscopy is used in various fields of research, including chemistry, physics, astronomy, and biology. It can be used to identify unknown substances, determine their concentration, and study their chemical reactions. It is also used to study the composition and properties of distant objects in space, such as stars and galaxies.

3. What types of spectroscopy are there?

There are several types of spectroscopy, including atomic spectroscopy, molecular spectroscopy, and mass spectrometry. Atomic spectroscopy involves the study of the energy levels and transitions of atoms, while molecular spectroscopy focuses on the energy levels and transitions of molecules. Mass spectrometry measures the mass-to-charge ratio of ions to identify and quantify substances.

4. How does spectroscopy work?

Spectroscopy works by passing light through a sample and recording the resulting spectrum. The spectrum is a plot of the intensity of light at different wavelengths, and it contains unique patterns that can be used to identify and analyze the sample. Different types of spectroscopy use different instruments and techniques to measure the spectrum, such as absorption, emission, or scattering of light.

5. What are some applications of spectroscopy?

Spectroscopy has many practical applications, such as in environmental monitoring, pharmaceutical analysis, and forensic science. It is also used in industrial processes, such as quality control and materials testing. In addition, spectroscopy is essential in the development of new materials and technologies, such as solar cells and LED lights.

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