Consider a mechanical system with one degree of freedom x, conjugate momentum p evolving under the Hamiltonian H(x, p). (a) State the definition of the density of phase states g(E) in the microcanonical ensemble. (b) State the definition of the canonical partition function z(B) for the same system in the canonical ensemble. (c) Assuming the energy values to be positive, show that +∞ z(B) g(ε)e-Be de.
Consider a mechanical system with one degree of freedom x, conjugate momentum p evolving under the Hamiltonian H(x, p). (a) State the definition of the density of phase states g(E) in the microcanonical ensemble. (b) State the definition of the canonical partition function z(B) for the same system in the canonical ensemble. (c) Assuming the energy values to be positive, show that +∞ z(B) g(ε)e-Be de.
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Transcribed Image Text:Consider a mechanical system with one degree of freedom x, conjugate
momentum p evolving under the Hamiltonian H(x, p).
(a) State the definition of the density of phase states g(E) in the microcanonical
ensemble.
(b) State the definition of the canonical partition function z(ß) for the same
system in the canonical ensemble.
(c) Assuming the energy values to be positive, show that
•+∞
z (B) = S₁
g(ɛ)e-ße dɛ.
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