Higher order Schrödinger equations

Rémi Carles (1) , Emmanuel Moulay (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 XLIM-SIC - SIC

The purpose of this paper is to provide higher order Schrödinger equations from a finite expansion approach. These equations converge toward the semirelativistic equation for particles whose norm of velocity vector is below c/√2 and are able to take into account some relativistic effectswith a certain accuracy in a sense that we define. So, it is possible to take into account some relativistic effects by using Schrödinger form equations, even if they cannot be considered as relativistic wave equations.

Domaines: Physique mathématique [math-ph]

Rémi Carles, Emmanuel Moulay. Higher order Schrödinger equations. Journal of Physics A: Mathematical and Theoretical, 2012, 45 (39), pp.395304. ⟨10.1088/1751-8113/45/39/395304⟩. ⟨hal-00776157⟩