Bug in FDM #73

Activity

1. MartinMikkelsen commented on Sep 2, 2026

   

   MartinMikkelsen

   on Sep 2, 2026

   Last edited by MartinMikkelsen

   Member

   More actions

   I assume this is the Hamiltonian from this discussion, #39
   I think the problem is due to a too small Krylov subspace in this line
   I will add a line to enlarge the Krylov subspace when the ArnoldiMethod does not converge in #75

   👀React with 👀1Reacted by Shuhei OHNO
2. MartinMikkelsen commented on Sep 3, 2026

   

   MartinMikkelsen

   on Sep 3, 2026

   Member

   More actions

   The enlarged Krylov subspace method seems to be working

   m₁    = 1.836
   m₂    = 1.836
   σσ   = -3
   l      = 0
   m      = 0
   Λ     = 0.8321
   λ     = 0.1653
   p      = 1
   κ     = 0.5069
   κκ    = 1.8609
   A      = 1.6553
   B      = 0.2204
   μ     = 1 / (1/m₁ + 1/m₂) # reduction mass
   r₀     = A*(2*m₁*m₂/(m₁+m₂))^(-B)
   H = Hamiltonian(
                     RestEnergy(c=1, m=m₁),
                     RestEnergy(c=1, m=m₂),
                     Kinetic(hbar=1, m=μ),
                     Coulomb(-κ),
                     Linear(λ),
                     Constant(-Λ),
                     Gaussian(2*π*κκ/3/m₁/m₂ / ((sqrt(π)*r₀)^3) * σσ, 1/r₀^2))
   
   FDM = FiniteDifferenceMethod(Δr=0.01, rₘₐₓ=100.0, R=0.01:0.01:100.0, l=0, direction=:c, solver=:ArnoldiMethod)
   
   println(solve(H, FDM, info=0, nₘₐₓ=4).E)

   which prints

   [3.005250358496244, 3.6082255845239786, 4.013370356782439, 4.353297108700312]

   👀React with 👀1Reacted by Shuhei OHNO
3. ohno

   closed this as completedin 3409369on Sep 3, 2026