Born-von Karman 1D chain dispersion omega^2 = (4 K/m) sin^2(ka/2); linear-recurrence

Layer 1 — Physicsin the materials-physics subtree

Born-von Karman lattice dynamics framework (Born-von Karman 1912 Phys Z 13, 297). Setup: 1D chain of N identical atoms (mass m, equilibrium spacing a) coupled by linear springs of stiffness K obeys discrete-difference equation m d^2…

Related concepts

Linear recurrence a_{n+k} + c_{k-1}a_{n+k-1} + ... = 0: characteristic-poly solution
Theorem: omega(k = pi/a)^2 - 4K/m = 0 (Born-von Karman Brillouin-zone-edge max frequency)

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