Matrix Formulation of the Eigenvalue Problem

Hyunju Lee, Kyungtaek Jun

Yousef Azizi

We use the frustrated XY model approximation of BEC in a rotating optical lattice and formulate the problem of the ground state in terms of eigenvectors and eigenvalues of frustrated adjacency matrix (coupling matrix). By using this formulation, we show that there is a lower bound for ground state energy in terms of maximum eigenvalue of this matrix.

Osama M. Raisuddin, Suvranu De

Wolfgang Ernst Friederich Pauli

Stefano De Leo, Gisele Cristina Ducati

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.

Willi-Hans Steeb