Calculation of eigens with geometrical algebra rotors

Presenter: Arturas Acus, Vilnius University, Lithuania

Joint work with Adolfas Dargys

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 geometrical algebra rotor equation, where the bivector in exponential rotor is constructed from two vectors, one is basis vector aligned with the quantization axis and the other comes from the rearrangement of the Hamiltonian in geometric algebra form. A number of fully elaborated examples are presented in $\textit{Cl}_{3,0}$ algebra (monolayer graphene and spin in the quantum well) and $\textit{Cl}_{3,1}$ algebra (two coupled two-level atoms and bilayer graphene).