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Basic Structures of RelativisticWave Functions

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Abstract

It is shown that relativistic many-body Hamiltonians and wave functions can be expressed systematically with Tracy-Singh products for partitioned matrices. The latter gives rise to the usual notion for a relativistic N-electron wave function: a column vector composed of 2N blocks, each of which consists of 2N components formed by the Kronecker products of N one-electron 2-spinors. Yet, the noncommutativity of the Tracy-Singh product dictates that the chosen serial ordering of electronic coordinates cannot be altered when antisymmetrizing a Tracy-Singh product of 4-spinors. It is further shown that such algebraic representation uncovers readily the internal symmetries of the relativistic Hamiltonians and wave functions, which are crucial for deriving the electron-electron coalescence conditions.

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Acknowledgements

The research of this work was supported by grants from the National Natural Science Foundation of China (Project Nos. 21033001, 21273011, 21290192, and 11471025).

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Sihong Shao

  2. Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing, People’s Republic of China

    Zhendong Li

  3. Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing, People’s Republic of China

    Wenjian Liu

Authors
  1. Sihong Shao
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  2. Zhendong Li
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  3. Wenjian Liu
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Corresponding authors

Correspondence to Sihong Shao or Zhendong Li .

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Editors and Affiliations

  1. Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering and Center for Computational Science and Engineering, Peking University, Beijing, China

    Wenjian Liu

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Shao, S., Li, Z., Liu, W. (2017). Basic Structures of RelativisticWave Functions. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40766-6_7

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