Institutionen för naturvetenskap och teknik

Research Seminar in Mathematics - A numerical damped oscillator approach to constrained Schrödinger equations

06 mars 2020 13:15 – 14:00 T1210, Teknikhuset

Detta föredrag kretsar kring en artikel som skall skickas in till en halvpedagogisk tidskrift snart. Detta är naturligtvis en 100%-ig garanti för att föredraget blir halvpedagogiskt, där ena hälften kommer från grundläggande matematik och andra hälften från grundläggande fysik.

Please contact Andrii Dmytryshyn if you have any questions regarding this seminar series.

Speaker

Magnus Ögren, Örebro universitet

Abstract

This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints.

We include three qualitative different numerical examples: the radial Schr\"{o}dinger equation for the hydrogen atom; the two-dimensional harmonic oscillator with degenerate excited states; and finally a non-linear Schr\"{o}dinger equation for rotating states.

The presented method is intuitive, with analogies in classical mechanics for damped oscillators, and easy to implement, either in own coding, or with software for dynamical systems.

Hence, we find it suitable to introduce it in a continuation course in quantum mechanics or generally in applied mathematics courses which contain computational parts.