Time dependent Schrödinger equation on arbitrary structured grids: Application to photoionization

Gordon, Daniel; Hafizi, B.

doi:10.1016/j.jcp.2012.05.021

Cited by 6 publications

(8 citation statements)

References 20 publications

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“…As pointed out in [1], when the time differencing in Eq. (3) is carried out semi-implicitly, and the Coulomb gauge is employed, the discretized time advance operator,…”

Section: Semi-implicit Advance and Operator Splittingmentioning

confidence: 93%

“…In a previous article [1], we described an algorithm for solving the time dependent Schrödinger equation (TDSE) in the Coulomb gauge, which strictly conserves probability on any structured grid with orthogonal basis vectors. The algorithm is particularly useful for simulating the photoionization of atoms, but can be applied equally well to any system where a non-relativistic electron is exposed to an arbitrary electromagnetic potential.…”

Section: Introductionmentioning

confidence: 99%

“…The scheme described in [1] is a natural candidate for computing Bohmian trajectories since it is based on a finite volume scheme similar to those used in computational hydrodynamics [9]. The finite volume method is constructed around the notion that the average value of some conserved quantity in a cell is updated by calculating the flux that carries that quantity through each cell wall.…”

Section: Introductionmentioning

confidence: 99%

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Amplitude flux, probability flux, and gauge invariance in the finite volume scheme for the Schrödinger equation

Gordon¹,

Hafizi²,

Landsman³

2015

Journal of Computational Physics

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The time dependent Schrödinger equation can be put in a probability conserving, gauge invariant form, on arbitrary structured grids via finite volume discretization. The gauge terms in the discrete system cancel with a portion of the amplitude flux to produce abbreviated flux functions. The resulting time translation operator is strictly unitary, and is compatible with an efficient operator splitting scheme that allows for multi-dimensional simulation with complex grid geometries. Moreover, the abbreviated amplitude flux is necessary to the construction of a conservative probability current. This construction turns out to be important when computing Bohmian trajectories in multi-dimensions. Bohmian trajectories are useful in the interpretation of quantum mechanical phenomena such as tunneling ionization, and provide a bridge between quantum and classical regimes.

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“…As pointed out in [1], when the time differencing in Eq. (3) is carried out semi-implicitly, and the Coulomb gauge is employed, the discretized time advance operator,…”

Section: Semi-implicit Advance and Operator Splittingmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Amplitude flux, probability flux, and gauge invariance in the finite volume scheme for the Schrödinger equation

Gordon¹,

Hafizi²,

Landsman³

2015

Journal of Computational Physics

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“…In the second, "microscopic", regime the interaction of the field with a single atom or molecule is examined in the quantum mechanical picture. This in principle requires solution of the time dependent Schrodinger equation (TDSE) using approximate analytical methods [8], finite-difference time domain (FDTD) numerical solutions [9], or by Floquet expansion schemes [10]. Although attempts have been made to couple Maxwell's Equations with a "microscopic" Schrodinger model [11], these simulations are computationally expensive and remain largely beyond reach at the time of this writing.…”

Section: Introductionmentioning

confidence: 99%

Strong-field ionization and gauge dependence of nonlocal potentials

Rensink

Antonsen

2016

Phys. Rev. A

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Nonlocal potential models have been used in place of the Coulomb potential in the Schrodinger equation as an efficient means of exploring high field laser-atom interaction in previous works. Although these models have found use in modeling phenomena including photo-ionization and ejected electron momentum spectra, they are known to break electromagnetic gauge invariance. This paper examines if there is a preferred gauge for the linear field response and photoionization characteristics of nonlocal atomic binding potentials in the length and velocity gauges. It is found that the length gauge is preferable for a wide range of parameters.

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“…The radius of the diagnostic sphere in all cases was 20 ground state radii (see Ref. 23 for a discussion of dependence on radius of diagnostic sphere).…”

mentioning

confidence: 99%

First Benchmark of Relativistic Photoionization Theories against 3D ab initio Simulation

2017

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Time dependent Schrödinger equation on arbitrary structured grids: Application to photoionization

Cited by 6 publications

References 20 publications

Amplitude flux, probability flux, and gauge invariance in the finite volume scheme for the Schrödinger equation

Amplitude flux, probability flux, and gauge invariance in the finite volume scheme for the Schrödinger equation

Strong-field ionization and gauge dependence of nonlocal potentials

First Benchmark of Relativistic Photoionization Theories against 3D ab initio Simulation

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