On Matrix Schr\"odinger Unitary Groups in Particular Representations of Finite Dimensional Quantum Dynamical Systems

Fredy Vides

On Matrix Schr\"odinger Unitary Groups in Particular Representations of Finite Dimensional Quantum Dynamical Systems

Quantum Algebra 2011-03-10 v4 Mathematical Physics math.MP Numerical Analysis

Authors: Fredy Vides

Abstract

In this paper we study some particular types of matrix Schr\"odinger semigroups of the form $\exp(-it\mathbb{H})$ where $\mathbb{H}\in M_N(\mathbf{C})$ is the Hamiltonian of a given quantum dynamical system modeled in the finite dimensional Hilbert space $\mathcal{H}$ . Once we have defined a particular matrix Schr\"odinger unitary group we perform some estimates for its approximation and its corresponding implementation in the numerical solution of the finite dimensional Schr\"odinger evolution equation to that it is related.

Keywords

matrix Schrödinger semigroup unitary group finite dimensional quantum system Hamiltonian numerical approximation Schrödinger evolution equation

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@article{arxiv.1102.4391,
  title  = {On Matrix Schr\"odinger Unitary Groups in Particular Representations of Finite Dimensional Quantum Dynamical Systems},
  author = {Fredy Vides},
  journal= {arXiv preprint arXiv:1102.4391},
  year   = {2011}
}

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10 pages, 1 figure

On Matrix Schr\"odinger Unitary Groups in Particular Representations of Finite Dimensional Quantum Dynamical Systems

Abstract

Keywords

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