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Lecture 18 Radioactive decay: Master equation approach

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Lecture 18

Radioactive decay: Master equation approach

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Radioactive decay, N

0

= 10, c = 0.5

The probability density functionP(N/N0,t) as a function of timet and the relative number of particlesN/N0. Note that this is a logarithm color plot, so0 on the color bar corresponds to1, and−1

- to10−1. White line, the the exponential decay,exp(−ct), is plotted in the one-standard deviation envelope (dashed yellow lines).

(3)

Radioactive decay, N

0

= 100,c = 0.5

The probability density functionP(N/N0,t) as a function of timet and the relative number of particlesN/N0. Note that this is a logarithm color plot, so0 on the color bar corresponds to1, and−1

- to10−1. White line, the the exponential decay,exp(−ct), is plotted in the one-standard deviation envelope (dashed yellow lines).

(4)

Radioactive decay, N

0

= 1000,c = 0.5

The probability density functionP(N/N0,t) as a function of timet and the relative number of particlesN/N0. Note that this is a logarithm color plot, so0 on the color bar corresponds to1, and−1

- to10−1. White line, the the exponential decay,exp(−ct), is plotted in the one-standard deviation envelope (dashed yellow lines).

(5)

Radioactive decay, N

0

= 100: propagation

This plot is obtained by propagation the initial state P(N,0) =δ(N−N0) with the matrix exponential B= exp(M ∗ 4t) (see the script above).4t= 0.02.

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