11 June, 2026

Notes

2026-10-30

On implementation of Hénon-Heiles

• I need to check the errors for the config variables
• I need to check for error in the explore.jl for bugs

These are two screen shots of the Hénon-Heiles potential

Left: a 3D and right a contour plot of the Hénon-Heiles potential.

Parameters

Parameter	Value	Units	Description
\(\alpha\)	2.0	—	Non-linear coupling strength
\(m\)	1.0	kg	Mass
\(\omega\)	1.0	1/s	Harmonic oscillator frequency

Lost Wonderers Thoughts:

I spend an hour raading “Postmoden Quantummechanics” [@heller1993postmodern].

Semiclassical approximation of quantum amplitudes have a universal form and is given by \[\psi(x)=\sum_n \sqrt{P_n(x)} \,\exp\Big\{i \varphi_n(x)/\hbar\Big\},\] with

• \(\varphi_n(x)\) – classical action along the \(n^\text{th}\) path reaching \(x\)

• \(P_n(x)\) – classical probability

Lines I considered interesting. What is it that makes the theory break down exactly?