- #1
morangta
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I am reading an article on the "energy surface" of a Hamiltonian. For a simple harmonic oscillator, I am assuming this "energy surface" has one (1) degree of freedom. For this case, the article states that the "dimensionality of phase space" = 2N = 2 and "dimensionality of the energy surface" = 2N-1 = 1.
Adjusting x gives H = ω (p + x). That's H = ω(p*p + x*x).
When I plot the energy surface for H, I get a 3-dimensional paraboloid plotted against the x-p plane. Or, lines of constant H are 2-dimensional circles in the p-x plane. What energy surface would be 2N-1 = one (1)-dimensional here? Am not trying to quibble about terminology here. Just want to know if I am missing something.
Thanks for reading.
Adjusting x gives H = ω (p + x). That's H = ω(p*p + x*x).
When I plot the energy surface for H, I get a 3-dimensional paraboloid plotted against the x-p plane. Or, lines of constant H are 2-dimensional circles in the p-x plane. What energy surface would be 2N-1 = one (1)-dimensional here? Am not trying to quibble about terminology here. Just want to know if I am missing something.
Thanks for reading.