Monday, 20 July 2020

homework and exercises - Analytical solution of Liouville's equation for classic harmonic oscillator


I'm interested in the analytical solution of the simple PDE:


ftmω2xfp+pmfx = 0.


With: f(x,p;t=0) = f0(x,p)arbitrary smooth,

x(t) = x0cos(ωt)+p0mωsin(ωt),
p(t) = p0cos(ωt)mωx0sin(ωt).


And x0,p0 constants.




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