A complete Hermitian operator basis set for any spin quantum number

A new Hermitian operator basis set for spins of any quantum number is presented for use in simulations of NMR experiments. The advantage with a Hermitian operator basis is that the Liouville-von Neumann equation, including relaxation with dynamic frequency shifts, is real. Real algebra makes numerical calculations faster and simplifies physical interpretation of the equation system as compared to complex algebra. The unity operator is included in the Hermitian operator basis, which makes it easy to rewrite the inhomogeneous Liouville-von Neumann equation into a homogeneous form. The unity operator also simplifies physical interpretation of the equation system for coupled spin systems.