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arXiv · 2103.11783

Various variational approximations of quantum dynamics

Caroline Lasser·Chunmei Su
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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 (1964) minimizes the residuum of the time-dependent Schr\"odinger equation, while the second one, originating from the lecture notes of Kramer--Saraceno (1981), imposes the stationarity of an action functional. We characterize both principles in terms of metric and a 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.

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Caroline Lasser, Chunmei Su. 2021-03-22. Various variational approximations of quantum dynamics. https://doi.org/10.1063/5.0088265

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