Introduction to Quantum Symmetries

Valter Moretti

Denis Bernard

Kira Joel, Davida Kollmar, Lea F. Santos

Quantum spin chains are prototype quantum many-body systems that are employed in the description of various complex physical phenomena. We provide an introduction to this subject by focusing on the time evolution of a Heisenberg spin-1/2 chain and interpreting the results based on the analysis of the eigenvalues, eigenstates, and symmetries of the system. We make available online all computer codes used to obtain our data.

Valter Moretti

Heinz Dietrich Doebner, V. K. Dobrev

T. Djama

We establish the quantum stationary Hamilton-Jacobi equation in 3-D and its solutions for three symmetrical potentials, Cartesian symmetry potential, spherical symmetry potential and cylindrical symmetry potential. For the two last potentials, a new interpretation of the Spin is proposed within the framework of trajectory representation.