The effect of cusps in time-dependent quantum mechanics

Abstract

Spatial cusps in initial wavefunctions can lead to non-analytic 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.

5 pages, 1 figure

References in corpus (4)

• Global fixed point proof of time-dependent density-functional theory
• Time-dependent current density functional theory on a lattice
• On the existence of effective potentials in time-dependent density functional theory
• Time dependent density functional theory for nonadiabatic electronic dynamics

Cited by in corpus (11)

• Time-dependent density functional theory for many-electron systems interacting with cavity photons
• A brief compendium of time-dependent density-functional theory
• Thermal density functional theory: Time-dependent linear response and approximate functionals from the fluctuation-dissipation theorem
• Existence, Uniqueness, and Construction of the Density-Potential Mapping in Time-Dependent Density-Functional Theory
• Time-dependent density functional theory on a lattice
• Time-dependent Orbital-free Density Functional Theory: Background and Pauli kernel approximations
• Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory
• A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density
• A Snapshot of Time-Dependent Density-Functional Theory
• Non-existence of Taylor expansion in time due to cusps
• Self-Similar Cusp Formation in Thin Liquid Films By Runaway Thermocapillary Forces