which is regular at the horizon. Further it can be shown that a certain boundary condition has to be fulfilled there. Although the probability density of the particle does not vanish within the event horizon we will omit this area. With the help of the above mentioned series expansion and boundary condition around the horizon we will get an initial value infinitesimal close to the event horizon from where a numerical integration procedure can be started. To start this integration procedure not directly at the event horizon is necessary because of the possibility to get to a solution which is not regular there. As in case of ordinary quantum mechanics the solution has to approach zero at infinity to represent a regular bound state that is normalizable. With this condition we can find the eigenstates by varying the energy as long as the wave function does vanish at infinity. The stationary states have complex energy eigenvalues as we are dealing with a non-hermitian Hamiltonian. The complexity of the energy eigenvalues is connected to the instability of the states and with the help of the imaginary part of the energy it is possible to determine the decay times. However, an exact 