# What is the name of this Hamiltonian?

1. Jul 29, 2014

### kinichi

Hello (and sorry for this stupid question),

Could someone tell me the name of this Hamiltonian

$$H = \left(\dfrac{p^2+q^2}{2}\right)^2$$

2. Jul 29, 2014

### Staff: Mentor

3. Jul 29, 2014

### kinichi

I'm just looking for the name that is called in the scientific literature. I am not looking for the Hamiltonian theory.

4. Jul 29, 2014

### Staff: Mentor

In the article, it shows a specific hamiltonian similar to yours and relates it to a "Heisenberg group" under the topic Sub-Riemannian manifolds.

Its unfortunate that the URL didn't directly jump there as expected.

5. Jul 29, 2014

### Staff: Mentor

Or maybe this one:

http://www.unige.ch/~hairer/poly_geoint/week1.pdf

6. Jul 29, 2014

### kinichi

Ok, Thank you jedishrfu.

However, there are subtle differences between these two Hamiltonians. "My" can be thought of as the Hamiltonian of the harmonic oscillator squared:

$$H = H_{HO}^2$$

where

$$H_{HO} = \dfrac{1}{2}(p^2+q^2)$$.

Last edited: Jul 29, 2014