(a) Show that the average position of the particle is given by fxe-Bu(2) dr fe-Bu(x) d. u(x) 4 where each integral is over the entire r axis. Figure 6.10. A one-dimensional po- tential well. The higher the temper- ature, the farther the particle will stray from the equilibrium point.
(a) Show that the average position of the particle is given by fxe-Bu(2) dr fe-Bu(x) d. u(x) 4 where each integral is over the entire r axis. Figure 6.10. A one-dimensional po- tential well. The higher the temper- ature, the farther the particle will stray from the equilibrium point.
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Consider a classical particle moving in a one-dimensional potential well u(x), as shown in Figure 6.10 (attached). The particle is in thermal equilibrium with a reservoir at temperature so the probabilities of its various states are determined by Boltzmann statistics.
Transcribed Image Text:(a) Show that the average position of the particle is given by
fxe-Bu(2) dr
fe-Bu(x) d.
u(x) 4
where each integral is over the entire r axis.
Figure 6.10. A one-dimensional po-
tential well. The higher the temper-
ature, the farther the particle will
stray from the equilibrium point.
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