Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 241–253 | Cite as

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 (HE) =  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.

Mathematics Subject Classification

Primary 15A18 Secondary 15A66 

Keywords

Geometric algebra Rotors Quantum mechanics Eigenspinors 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Semiconductor Physics Institute, Center for Physical Sciences and TechnologyVilniusLithuania
  2. 2.Institute of Theoretical Physics and AstronomyVilnius UniversityVilniusLithuania

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