  We investigate the occurrence of vibrational resonance in both classical and
quantum mechanical Morse oscillators driven by a biharmonic force. The
biharmonic force consists of two forces of widely different frequencies \omega
and \Omega with \Omega>>\omega. In the damped and biharmonically driven
classical Morse oscillator applying a theoretical approach we obtain an
analytical expression for the response amplitude at the low-frequency \omega.
We identify the conditions on the parameters for the occurrence of the
resonance. The system shows only one resonance and moreover at resonance the
response amplitude is 1/(d\omega) where d is the coefficient of linear damping.
When the amplitude of the high-frequency force is varied after resonance the
response amplitude does not decay to zero but approaches a nonzero limiting
value. We have observed that vibrational resonance occurs when the sinusoidal
force is replaced by a square-wave force. We also report the occurrence of
resonance and anti-resonance of transition probability of quantum mechanical
Morse oscillator in the presence of the biharmonic external field.
