def calculate_omega_matrix(states, Omega=1):
    """Calculate the matrix of transition frequencies.

    This function recieves a list of states and returns the corresponding
    omega_ij matrix, rescaled to units of Omega. These are understood to be
    absolute frequencies (as opposed angular frequencies).
    """
    N = len(states)
    omega = [[2*Pi*(states[i].nu-states[j].nu)/Omega
              for j in range(N)] for i in range(N)]

    return omega