Variational approach to the time-dependent Schrödinger-Newton equations

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.

14 pages, 7 figures

References in corpus (6)

• Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects
• The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
• Breather mode in the many-electron dynamics of semiconductor quantum wells
• A possible experimental test of quantized gravity
• Nonlinear dynamics of electron-positron clusters
• Solving the Anharmonic Oscillator: Tuning the Boundary Condition