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Show that if f(x) = Ac* where A and k are real constants, then f(x) satisfies: %3D d² f(x) + k° f(x) = 0 da

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter1: Matrices, Vectors, And Vector Calculus

Section: Chapter Questions

Problem 1.35P

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Concept explainers

Debye Theory of Solids

In solid-state physics, debye theory is used to estimate the phonons contributing to the specific heat capacity in a solid. It explains that the specific heat is a consequence of the vibrations of the atomic lattice of the solid, which is in contrast to the Einstein model. In the Einstein model, solids are treated as independent, non-interacting quantum harmonic oscillators. This model clearly explains the low-temperature dependence of the heat capacity, which is proportional to T3. This is known as Debye T3 law.

Question

Show that if f(x) = Ac* where A and k are real constants, then f(x) satisfies:
%3D
d²f(z) + k° f(x) = 0
da

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