Estimations of the errors between the evolving states generated by two Hamiltonians with the same initial state

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Abstract

Time evolution of a quantum system is described by Schrödinger equation with initial pure state, or von Neumann equation with initial mixed state. In this paper, we estimate the error between the evolving states generated by two Hamiltonians with the same initial pure state. Secondly, according to the method of operator–vector correspondence, we give a relation of the Schrödinger equation and von Neumann equation and then estimate the error between the evolving states generated by two Hamiltonians with the same initial mixed state.

Keywords

Schrödinger equation von Neumann equation Error estimation Time evolution 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11771009, 11601300, 11571213) and the Fundamental Research Funds for the Central Universities (GK201703093).

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Authors and Affiliations

  1. 1.School of Ethnic EducationShaanxi Normal UniversityXi’anChina
  2. 2.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina

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