Complex potential and its effects on bound states

The coupling of bound states in a single-particle effective Hamiltonian through the addition of a negative definite imaginary potential is studied, both in a stationary and in a time-dependent formalism.Corresponding physical cases where this coupling is relevant are exhibited.Properties of the imaginary coupling matrix in the representation of the eigenstates of the real Hamiltonian are investigated.Consequences of these properties on the level widths and level shifts are exhibited on the two level case.Non trivial results, like forbidden values of the widths and level attraction are underlined.The conditions for the validity of the weak coupling approximation are examined.In the time-dependent problem, the typical time evolution patterns are illustrated both in the two level case and in the more realistic case of charmonium decay.When the initial state is an eigenstate of the real part of the Hamiltonian, it is shown that mixing of decay modes and quantum interference arise as consequences of the non diagonal imaginary coupling.Finally, the non locality of the imaginary potential corresponding to a diagonal imaginary coupling matrix in the state representation is also briefly studied and illustrated.