The time-dependent Schrödinger equation with piecewise constant potentials

DOI10.1017/S0956792518000475zbMath1506.35187arXiv1709.02450OpenAlexW2963947812MaRDI QIDQ5056692

Natalie E. Sheils, Bernard Deconinck

Publication date: 8 December 2022

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02450

zbMATH Keywords

Schrödinger equationFokas methodunified transform method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Integral representations of solutions to PDEs (35C15) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) PDEs in connection with quantum mechanics (35Q40) Solutions to PDEs in closed form (35C05) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (5)

Linear evolution equations on the half-line with dynamic boundary conditions ⋮ The linear KdV equation with an interface ⋮ Integral representations for the double-diffusivity system on the half-line ⋮ Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks ⋮ Solving the heat equation with variable thermal conductivity

Cites Work

• Fokas transform method for a brain tumor invasion model with heterogeneous diffusion in 1+1 dimensions
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