VALIDITY OF VARIATIONAL PROCEDURES FOR RESONANT STATES

The behavior of variational procedures for bound states is well unders tood, when using harmonic oscillator wave functions whose frequency om ega is the only parameter. The same procedure, when applied to problem s that have resonant states, shows a completely different behavior. By analyzing the s-wave problem for a cavity potential of the form b' de lta(r' - a), we show that, as a function of omega, ii gives rise to pl ateaus that correspond to the real part of the resonant energies, assu ming values of b' related to very narrow resonances compared with thei r separations. If the latter condition holds, the procedure seems gene ralizable to other types of potentials. (C) 1996 American Association of Physics Teachers.