The fast Hankel transform as a tool in the solution of the time dependent Schrödinger equation

DOI10.1016/0021-9991(85)90112-3zbMath0578.65127OpenAlexW2149968002MaRDI QIDQ1066650

Ronnie Kosloff, Rob H. Bisseling

Publication date: 1985

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(85)90112-3

zbMATH Keywords

fast Fourier transformSchrödinger equationharmonic oscillatorFourier methodhyperspherical coordinatesfast Hankel transform

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications to the sciences (65Z05)

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Reducing dimensionality to model 2D rotating and standing waves in a delayed nonlinear optical system with thin annulus aperture ⋮ Absorbing boundaries for wave propagation problems ⋮ Time-dependent solution of the Liouville-von Neumann equation: Non-dissipative evolution ⋮ Time-dependent wavepacket algorithm for inelastic molecule-molecule scattering ⋮ Solution of the time-dependent Schrödinger equation employing a basis of explicit discrete-coordinate eigenfunctions: Spherical and azimuthal symmetry, adiabaticity, and multiphoton excitation of a rotating Morse oscillator ⋮ A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions ⋮ Orthogonal fast spherical Bessel transform on uniform grid ⋮ Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves ⋮ Numerical evaluation and error analysis of many different oscillatory Bessel transforms via confluent hypergeometric function ⋮ A numerical evaluation of the Hankel transform of bandlimited functions ⋮ Numerical evaluation of spherical Bessel transforms via fast Fourier transforms

Cites Work

• A Fourier method solution for the time dependent Schrödinger equation as a tool in molecular dynamics
• Spectral methods for multi-dimensional diffusion problems
• Spectral multigrid methods for elliptic equations
• Numerical Fourier and Bessel transforms in logarithmic variables
• A numerical and theoretical study of certain nonlinear wave phenomena
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