1. According to the fundamental assumption of statistical thermodynamics, the probability P(N, S) for a large...

 

Transcribed Image Text:

1. According to the fundamental assumption of statistical thermodynamics, the probability P(N, S) for a large N binary magnet system with spin excess 2s is given by P(N, s) = (¹/2 exp(-2²). (a) Plot P(N,s) for N = 10, 1000, and 100000: In order to appreciate the very nature of Gaussian statistics, you need to plot P(N,s) for |s| ≤ N/2. N N 202. (b) The Gaussian standard deviation of a Gaussian distribution- exp(- is parametrized by . Therefore, o of P(N,s) is √N/2. Show that o² = ((s-(s))²) = (s²) - (s)² = N/4 by direct calculation. (c) How is o related to the full width half maximum (FWHM)? 1 1. According to the fundamental assumption of statistical thermodynamics, the probability P(N, S) for a large N binary magnet system with spin excess 2s is given by P(N, s) = (¹/2 exp(-2²). (a) Plot P(N,s) for N = 10, 1000, and 100000: In order to appreciate the very nature of Gaussian statistics, you need to plot P(N,s) for |s| ≤ N/2. N N 202. (b) The Gaussian standard deviation of a Gaussian distribution- exp(- is parametrized by . Therefore, o of P(N,s) is √N/2. Show that o² = ((s-(s))²) = (s²) - (s)² = N/4 by direct calculation. (c) How is o related to the full width half maximum (FWHM)? 1

Answer rating: 100% (QA)

Solution az Given that ... View the full answer