What Units Are Used in Solid State Physics Equations?

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The discussion centers on the units used in solid state physics, specifically addressing the equation \(\Lambda a \sim 1\), where \(\Lambda\) represents a momentum cutoff and \(a\) denotes lattice spacing. Participants clarify that in solid state physics, momentum is often expressed in terms of the wave-vector \(k\), with the relationship \(p = \hbar k\), where \(\hbar\) is the reduced Planck constant. The conversation emphasizes that while atomic units are commonly used, the equation's validity hinges on the context of the physical system being analyzed.

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zakk87
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I'm having some troubles understanding the unit used in solid state physics. In a paper I read

\Lambda a \sim 1

where \Lambda is a momentum cutoff and a is the lattice spacing of a crystal. Questions:

1) What kind of units are customarily used in solid state physics scientific articles? Can I be confident that they are atomic units?

2) The aforementioned equation is not correct as far as the units of measure are concerned. If this was solid state physics, I would say that one could set the speed of light and the Planck constant to 1 and make the equation correct. However in a low energy treatment in solid state physics, I don't see the point in using the speed of light or the Planck constant, and making the physics of the system dependent upon these quantities.

Thanks in advance for your answers.
 
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I don't know what you mean by "atomic units".
However the momentum of electrons in crystals may be given or plotted in terms of "k", the wave-vector.
The momentum p can be written as p=\hbar k where k is the wavevector.
Your capital lambda is probably the maximum value of k along that direction.
It has units of inverse meter.
 

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