Packages

#Packages

Finite-elements, discrete-variable representation for radial coordinate (https://github.com/jagot/FEDVR.jl); depends on https://github.com/jagot/BlockMaps.jl

Convenience functions for generating single-active electron Hamiltonians (https://github.com/jagot/Quantum.jl); depends on

Will at some point probably leverage https://github.com/JuliaApproximation/ApproxFun.jl

Commutator-free Magnus propagators using Hermitian Lanczos exponentiators (https://github.com/jagot/Magns us.jl), will at some point be replaced by DifferentialEquations.jl + Expokit.jl

Simplifies generating laser pulses (https://github.com/jagot/SimpleFields.jl)

Parameters

#Parameters
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8 Hartrees ~ 240 eV

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Spectrum of the Hamiltonian

#Spectrum-of-the-Hamiltonian

This function plots the residuals as a function of eigenvalue iteration in the Jacobi–Davidson eigensolver

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Common settings for eigenvalue decomposition, for instance we want eigenvalues close to the ground state energy, -0.5 Ha ~ 13.6 eV

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Hamiltonians and ground state for time stepping

#Hamiltonians-and-ground-state-for-time-stepping
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Electric field

#Electric-field
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Steps per cycle (ndt) and total amount of steps.

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Commutator-free Magnus propagator of 4th order for matrices of the type @@0@@

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Solve the TDSE

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What is missing is an absorbing boundary at @@0@@ = rmax, the exception of this leads to unphysical reflections. This will probably be implemented using exterior complex scaling (ECS) as described in https://journals.aps.org/pra/abstract/10.1103/PhysRevA.62.032706

The Hamiltonian will not be Hermitian then, outside a certain radius, but complex-symmetric (without the complex scaling, the Hamiltonian is real-symmetric and thus Hermitian).