# 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).