Effect of Cusps in Time-Dependent Quantum Mechanics

2011/09/30 by Zeng-hui Yang, Neepa T. Maitra, Kieron Burke · 15 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Classical mechanics #Mathematical analysis #Mathematics #Physics #Quantum Mechanics and Applications #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Taylor series #Wave function #cond-mat.mtrl-sci #cond-mat.other #physics.atom-ph #quant-ph

paper · pdf · doi:10.1103/physrevlett.108.063003

published in Physical Review Letters 108(6), 063003 (American Physical Society) · 5 pages, 1 figure

arxiv created 2011/09/30 · openalex publication_date 2012/02/09 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Within nonrelativistic quantum mechanics, spatial cusps in initial wave functions can lead to nonanalytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time analytic.

Citations

• Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v -representability problem
• Electronic excitations: density-functional versus many-body Green’s-function approaches
• Time-Dependent Density Functional Theory for Open Quantum Systems with Unitary Propagation
• Self-Consistent Equations Including Exchange and Correlation Effects

Cited by

• Time-Dependent Density Functional Theory for Many-Electron Systems Interacting with Cavity Photons