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Momentum Shell

Energy shell of a harmonic oscillator in phase space. Every microstate of fixed energy EE lies on the ellipse, whose semi-axes 2E/m\sqrt{2E/m} and 2E/k\sqrt{2E/k} are set by the mass and the spring constant. Counting the states in a thin shell around this curve is what defines the microcanonical entropy. See also ergodic, which adds a trajectory filling the shell.


Momentum Shell

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  momentum-shell.typ (11 lines)