Pang Chunping, Liu Wenjie, Zhang Xuelin, Wang Hanquan
In recent years, significant progress has been made in numerical studies of ground-state solutions for Bose-Einstein condensates. Building upon previous research, this paper proposes a novel computational scheme: first, the constrained energy functional minimization problem in function space is transformed into an unconstrained optimization problem in parameter space via a reparameterization approach; then, by incorporating derivative approximation and numerical integration techniques, the continuous optimization problem is discretized into a standard finite-dimensional formulation; finally, the quasi-Newton method is employed for efficient numerical solution. Systematic numerical experiments in one, two, and three dimensions validate the computational accuracy and effectiveness of the proposed method. The results demonstrate that the reparameterization scheme accurately captures the spatial localization characteristics of quantum systems when solving the ground-state problem of Bose-Einstein condensates, exhibiting excellent numerical stability and broad applicability.
