Shape of Potential & Wave Vector 'K': Explained

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    Potentials Shapes
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Discussion Overview

The discussion revolves around the shapes of potentials in quantum mechanics, particularly in relation to nuclear potentials, and the significance of the wave vector 'K' and K-space in band theory. Participants explore theoretical aspects and physical interpretations without reaching definitive conclusions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants inquire about how the shape of a potential is determined, specifically questioning the nature of nuclear potentials.
  • One participant suggests that light nuclei have approximately parabolic potentials, while heavy nuclei like uranium may be modeled using a square well combined with Coulomb repulsion.
  • There is a discussion on the wave vector 'K', with one participant stating that it is related to the wavelength and momentum of a wave, noting the mathematical representation of the wave function.
  • Another participant emphasizes that the k-vector indicates the direction of wave propagation and its magnitude correlates with momentum and wavelength.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the physical importance of the wave vector 'K' and its implications in band theory. Multiple viewpoints on the shape of nuclear potentials are presented, indicating a lack of consensus.

Contextual Notes

Participants do not fully resolve the implications of the wave vector 'K' in band theory, nor do they clarify the assumptions underlying the shapes of nuclear potentials.

photon79
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shapes of potentials!

Hi all..

1)we have,for example,rectangular, square well, well type etc potentials. How is the shape of a potential is determined? What is the shape of the nucleus potential?

2)I am unable to get the physical importence of the wave vector 'K' and K-space in band theory!
 
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photon79 said:
1) What is the shape of the nucleus potential?
In light nuclei it as approximately parabolic.

In heavy nuclei (uranium), alpha particles are often modeled as moving in a square well + Coulomb repulsion.
2)I am unable to get the physical importence of the wave vector 'K' and K-space in band theory!
Ask your teacher to explain it one more time.
 
The wave vector k is identically to: abs(k)=2pi/lambda and momentum=h(bar)k. So you can think of it as the inverse of the wave length of a wave. Its more confortable to write psy(x)=exp(kx) than psy(x)=exp(2pi/lambda*x).
If we work in more dimensions k must be a vector and as you can see in the wave function lambda must therefor also be a vector. And 2pi/VECTOR seems to look strange.

You see?
 
The k-vector gives the direction of wave propagation. The magnitude of k is proportional to the momentum of the wave, which as we know is related to the wavelength.

Claude.
 

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