Analytically solvable Hamiltonians for quantum two-level systems and their dynamics

A simple systematic way of obtaining analytically solvable Hamiltonians forquantum two-level systems is presented. In this method, a time-dependentHamiltonian and the resulting unitary evolution operator are connectedthrough an arbitrary function of time, furnishing us with new analyticallysolvable cases. The method is surprisingly simple, direct, and transparent andis applicable to a wide class of two-level Hamiltonians with no involvedconstraint on the input function. A few examples illustrate how the methodleads to simple solvable Hamiltonians and dynamics.