Effective Hamiltonians in quantum physics: resonances and geometric   phase
  Effective Hamiltonians are often used in quantum physics, both in time dependent and time independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian. 
A.R.P.Rau and D.Uskov