What is the meaning of k in E(k) diagram?

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Discussion Overview

The discussion centers on the physical interpretation of the parameter "k" in the context of E(k) diagrams, particularly in semiconductor physics. Participants explore its meaning, relationship to momentum, and the nature of energy represented in these diagrams.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the physical meaning of "k," noting that it can be real or complex and questioning whether only the real part corresponds to wavelength.
  • Another participant asserts that "k" is the wavenumber and relates it to momentum through the equation p=hbar*k.
  • A participant seeks clarification on whether E(k) refers to kinetic energy, potential energy, or total energy, suggesting it might be the kinetic part due to its relation to momentum.
  • One participant confirms that E(k) represents kinetic energy.
  • A later reply provides a formula for E(k) and notes that while E can be considered as kinetic energy, the zero energy value corresponds to potential energy, indicating a more complex relationship.

Areas of Agreement / Disagreement

Participants generally agree that "k" is related to momentum and that E(k) pertains to kinetic energy, but there is some uncertainty regarding the interpretation of complex values of "k" and the full nature of energy represented in E(k).

Contextual Notes

The discussion includes assumptions about the definitions of energy types and the implications of complex values of "k," which remain unresolved.

Nemanja989
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hello :) ,

like I said in the title of this topic I am confused about physical interpretation of physical quantity ˝k˝. I came to this problem while doing the first chapter of book in semiconductor physics, where authors simply define some value (parameter) ˝k˝ thanks to solution of some equation, but they didn't give any meaning for ˝k˝. Only what they said is that ˝k˝ can be real or complex.

First I thought it can be understood through wavelength of electron (particle), but since it can be complex I'm not sure. Perhaps only Re{k} corresponds to wavelength?..

So, if anybody can help, please be my guest :)..
 
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k is the wavenumber, or more importantly, related to the momentum (crystal momentum) in the E(k) dispersion diagram.

p=hbar*k

Zz.
 
Ok, thanks :) .

Just to ask one more thing. I'm not so sure what energy we are talking about when we say E(k)? Is it kinetic energy or potential or maybe whole energy of electron (Ek+U)?
I suppose that it is kinetic part since it is related to the momentum of electron..
 
It's kinetic energy.

Zz.
 
E(k)=(hbar*k)^2/(2m)+Vo

In the E(k) diagrams (dispertion curve) E can be considered as the kinetic energy only, but the zero energy value corresponds to the potential energy Vo, so, it's not actually zero.
 

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