Unitary Integration of Quantum Liouville-Bloch Equations
A. R. P. Rau · Physical Review Letters · 1998
The Liouville-Bloch equation for a general spin $j$ in time-dependent external fields is solved as a unitary product of exponential operators. Operator noncommutativity is explicitly handled so as to leave behind a set of first-order differential equations for classical functions of time. Of these, only one is nontrivial and, once solved, the remaining yield to simple quadrature. Exact solutions or perturbative expansions of the classical equations can be used for analytical or numerical integration of the quantal equations.