A variational approach for linearly dependent moving bases in quantum
dynamics: application to Gaussian functions
- URL: http://arxiv.org/abs/2205.02358v1
- Date: Wed, 4 May 2022 23:41:09 GMT
- Title: A variational approach for linearly dependent moving bases in quantum
dynamics: application to Gaussian functions
- Authors: Lo\"ic Joubert-Doriol
- Abstract summary: We present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr"odinger equation.
We show that the resulting dynamics converges to the exact one and is unitary by construction.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this paper, we present a variational treatment of the linear dependence
for a non-orthogonal time-dependent basis set in solving the Schr\"odinger
equation. The method is based on: i) the definition of a linearly independent
working space, and ii) a variational construction of the propagator over finite
time-steps. The second point allows the method to properly account for changes
in the dimensionality of the working space along the time evolution. In
particular, the time evolution is represented by a semi-unitary transformation.
Tests are done on a quartic double-well potential with Gaussian basis function
whose centers evolve according to classical equations of motion. We show that
the resulting dynamics converges to the exact one and is unitary by
construction.
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