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Hamilton’s equations, real and complex, and a colloquium

Posted by: Brenton LeMesurier | 2011/10/22 | No Comment |

UPDATE: it works now! Details coming in a future post.

I would like to be able to can now post mathematical stuff like the following here, but the mathematical notation cannot be displayed nicely, so instead see it at http://brentonlemesurier.wordpress.com:
posting to a blog hosted at WordPress using the WordPress blogging software is the only option I currently know of that allows mathematical notation. I am thinking of moving my professional web presence there, for the sake of being about to talk mathematically.

On the other hand, most people who understand the math probably also understand the latex-like notation used for it below, or should learn latex as a critical communication tool in mathematics and related sciences, so here goes:

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As background for the colloquium that I will be giving at the College on Friday November 18 (details at math.cofc.edu/colloquium), here are the canonical forms of Hamiltonian equations, in both the most familiar real form

\displaystyle \frac{d q_n}{d t} = \frac{\partial H}{\partial p_n}, \quad \frac{d p_n}{d t} = -\frac{\partial H}{\partial q_n}

and the complex form,

\displaystyle \frac{d z_n}{d t} = i \frac{\partial H}{\partial z_n^*}, \quad \frac{d z_n^*}{d t} = -i\frac{\partial H}{\partial z_n}

which is often convenient in situations involving either Schroedinger’s equation or other conservative equations involving complex quantities, such as in optics.

under: mathematics, wordpress blog usage

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