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| The '''Born–von Karman boundary condition''' are [[periodic boundary conditions]] which impose the restriction that a [[wave function]] must be [[periodic function|periodic]] on a certain [[Bravais lattice]]. (Named after [[Max Born]] and [[Theodore Von Karman]]). This condition is often applied in [[solid state physics]] to model an ideal [[crystal]].
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| The condition can be stated as
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| : <math> \psi(\bold{r}+N_i \bold{a}_i)=\psi(\bold{r}), \, </math>
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| where ''i'' runs over the [[dimension]]s of the Bravais lattice, the '''a'''<sub>''i''</sub> are the primitive vectors of the lattice, and the ''N<sub>i</sub>'' are any integers (assuming the lattice is infinite). This definition can be used to show that
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| : <math> \psi(\bold{r}+\bold{T})=\psi(\bold{r}) </math>
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| for any lattice translation vector '''T''' such that:
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| : <math> \bold{T} = \sum_i N_i \bold{a}_i. </math> | |
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| Note, however, the Born–von Karman boundary conditions are useful when ''N<sub>i</sub>'' are large (infinite).
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| The Born–von Karman boundary condition is important in solid state physics for analyzing many features of crystals, such as [[diffraction]] and the [[Electronic band structure|band gap]]. Modeling the [[potential]] of a crystal as a periodic function with the Born–von Karman boundary condition and plugging in [[Schrödinger equation|Schrödinger's equation]] results in a proof of [[Bloch wave|Bloch's theorem]], which is particularly important in understanding the band structure of crystals.
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| ==References==
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| {{reflist}}
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| *{{Cite book | last1 = Ashcroft | first1 = Neil W. | last2 = Mermin | first2 = N. David | title = Solid state phys | year = 1976 | publisher = New York, Holt, Rinehart and Winston | isbn = 978-0-03-083993-1 | pages = 135 }}
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| *{{cite journal|last = Leighton|first = Robert B.|title = The Vibrational Spectrum and Specific Heat of a Face-Centered Cubic Crystal | year = 1948|journal = [[Reviews of Modern Physics]]|volume = 20|issue = 1|pages = 165–174|doi = 10.1103/RevModPhys.20.165|bibcode=1948RvMP...20..165L}}
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| ==External links==
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| {{DEFAULTSORT:Born-von Karman boundary condition}}
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| [[Category:Condensed matter physics]]
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| [[Category:Boundary conditions]]
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| {{physics-stub}}
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Hi there. Allow me begin by introducing the writer, her title is Sophia. The preferred pastime for him and his children is to perform lacross and he would never give it up. I am currently a travel agent. For a whilst I've been in Alaska but I will have to move in a yr or two.
My blog - free psychic readings, http://www.publicpledge.com/blogs/post/7034,