Demos.HenonHeiles.Bound2D
Quasi-bound states of a Henon-Heiles potential (in 2D)
Classical bound motion in the two-dimensional Henon-Heiles system is only possible for energies not exceeding that of the saddle points. Corresponding quantum mechanical "quasi-bound" states can be detected using the Fourier grid Hamiltonian algorithm implemented in WavePacket. Note, however, that these states are resonances which can decay via tunneling through the barriers at the saddles.
For the present simulations, we choose A=1 and λ=1/(4*√5), see work by M.J.Davis and E.J. Heller and by J.P.Kuska and C. Herrmann (Physik Journal, pp. 23-25, Sept. 2005). There are exactly 100 "quasi-bound" states below the saddle height of 40/3. All energies obtained with the FGH algorithm as implemented in WavePacket agree very well with those in the above mentioned work except for one "scattering" state (n=92).
