Prove that (5.6.15) is a solution to the diffusion equation (5.6.14) with the initial condition n(x(vector), 0)

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Prove that (5.6.15) is a solution to the diffusion equation (5.6.14) with the initial condition n(x(vector), 0) = δ(x(vector)). Show that it conserves the total number of particles.

What is the full width at half maximum of this distribution as a function of time?

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Solid State Physics Essential Concepts

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Question Posted: Aug 23, 2023 03:04 AM

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Prove that (5.6.15) is a solution to the diffusion equation (5.6.14) with the initial condition n(x(vector), 0)

Question:

n(x, t) = 1 (4π Dt)3/2ex²/4D1 (5.6.15)

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Let r Since the initial condition is spherically symmetric so will the solution be We therefore take ...View the full answer

Solid State Physics Essential Concepts

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