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Calculation of Quantum Eigens with Geometrical Algebra Rotors

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Abstract

A practical computational method to find the eigenvalues and eigenspinors of quantum mechanical Hamiltonian is presented. The method is based on reduction of the eigenvalue equation to well known geometrical algebra rotor equation and, therefore, allows to replace the usual det (H − E) =  0 quantization condition by much simple vector norm preserving requirement. In order to show how it works in practice a number of examples are worked out in Cl 3,0 (monolayer graphene and spin in the quantum well) and in Cl 3,1 (two coupled two-level atoms and bilayer graphene) algebras.

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Authors and Affiliations

  1. Semiconductor Physics Institute, Center for Physical Sciences and Technology, A. Goštauto 11, 01108, Vilnius, Lithuania

    A. Dargys

  2. Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, 01108, Vilnius, Lithuania

    A. Acus

Authors
  1. A. Dargys
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  2. A. Acus
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Correspondence to A. Acus.

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Dargys, A., Acus, A. Calculation of Quantum Eigens with Geometrical Algebra Rotors. Adv. Appl. Clifford Algebras 27, 241–253 (2017). https://doi.org/10.1007/s00006-015-0549-6

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  • DOI: https://doi.org/10.1007/s00006-015-0549-6

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