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arXiv · 1210.7645

Variational approach to the time-dependent Schrödinger-Newton equations

Giovanni Manfredi·Paul-Antoine Hervieux·Fernando Haas
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Abstract

Using a variational approach based on a Lagrangian formulation and Gaussian trial functions, we derive a simple dynamical system that captures the main features of the time-dependent Schrödinger-Newton equations. With little analytical or numerical effort, the model furnishes information on the ground state density and energy eigenvalue, the linear frequencies, as well as the nonlinear long-time behaviour. Our results are in good agreement with those obtained through analytical estimates or numerical simulations of the full Schrödinger-Newton equations.

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Giovanni Manfredi, Paul-Antoine Hervieux, Fernando Haas. 2013-03-12. Variational approach to the time-dependent Schrödinger-Newton equations. https://doi.org/10.1088/0264-9381%2F30%2F7%2F075006

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