An Introduction to Thermal Physics
An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 6.2, Problem 19P
To determine

The formula for the standard deviation of the energy of a system of N identical harmonic oscillators in the high temperature limit is to be calculated. The measure of the fractional fluctuation in energy.

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Starting from equation 7.83 attached, derive a formula for the density of states of a photon gas (or any other gas of ultrarelativistic particles having two polarization states). Sketch this function.
6.2 Let the "uniform" ensemble of energy E be defined as the ensemble of all systems of the given type with energy less than E. The equivalence between (6.29) and (6.27) means that we should obtain the same thermodynamic functions from the "uniform" ensemble of energy E as from the microcanonical ensemble of energy E. In particular, the internal energy is E in both ensembles. Explain why this seemingly paradoxical result is true.
Suppose a particle of mass m and charge q is in a one-dimensional harmonic oscillator potential with natural frequency wo. For times t > 0 a time-dependent potential of the form V₁(x,t) = εx cos(wt) is turned on. Assume the system starts in an initial state In). 1. Find the transitionn probability from initial state (n) to a state \n') with n' ‡ n. 2. Find the transition rate (probability per unit time) for the transition (n) → \n'). Note: (n'|x|n)= = ħ 2mwo (√√n +18n',n+1 + √ñdn',n−1).
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