Various variational approximations of quantum dynamics

Caroline Lasser, Chunmei Su

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan [Mol. Phys. 8, 39-44 (1964)], minimizes the residuum of the time-dependent Schrödinger equation, while the second one, originating from the lecture notes of Kramer and Saraceno [Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics Vol. 140 (Springer, Berlin, 1981)], imposes the stationarity of an action functional. We characterize both principles in terms of metric and symplectic orthogonality conditions, consider their conservation properties, and derive an elementary a posteriori error estimate. As an application, we revisit the time-dependent Hartree approximation and frozen Gaussian wave packets.

Original languageEnglish
Article number072107
JournalJournal of Mathematical Physics
Volume63
Issue number7
DOIs
StatePublished - 1 Jul 2022

Fingerprint

Dive into the research topics of 'Various variational approximations of quantum dynamics'. Together they form a unique fingerprint.

Cite this