(20.7) The energy E of a system of three independent harmonic oscillators is given by 1 E = (Nx + ½ )ħw + (ny + 1⁄2)ħw + (n = + 12/2)ħw. (20.49) Show that the partition function Z is given by (20.50) where ZSHO is the partition function of a simple harmonic oscillator given in eqn 20.3. Hence show that the Helmholtz function is given by e-Shw), F = Z = 3 ZSHO, 3 ħw + 3kBT ln(1 1 (20.51) and that the heat capacity tends to 3kB at high temperature.
(20.7) The energy E of a system of three independent harmonic oscillators is given by 1 E = (Nx + ½ )ħw + (ny + 1⁄2)ħw + (n = + 12/2)ħw. (20.49) Show that the partition function Z is given by (20.50) where ZSHO is the partition function of a simple harmonic oscillator given in eqn 20.3. Hence show that the Helmholtz function is given by e-Shw), F = Z = 3 ZSHO, 3 ħw + 3kBT ln(1 1 (20.51) and that the heat capacity tends to 3kB at high temperature.
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Transcribed Image Text:(20.7) The energy E of a system of three independent
harmonic oscillators is given by
1
E = (nx + = 2 ) hw + (ny + = 2 ) hw + (n₂ + 2/2 ) hw.
(20.49)
Show that the partition function Z is given by
(20.50)
where ZSHO is the partition function of a simple
harmonic oscillator given in eqn 20.3. Hence show
that the Helmholtz function is given by
F =
3
Z = ZŠHO,
3
ħw + 3kBT ln(1 - e-Bhw), (20.51)
and that the heat capacity tends to 3kB at high
temperature.
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