The explicit coordinate representation of coherent states for the Morse oscillator is derived and discussed, in the limit that the potential well is deep. Without this limit, such states can only be written as a finite sum that does evolve coherently but in a dilated time.
We obtain the exact, normalized, closed-form eigenfunctions for the one-dimensional Morse oscillator, as well as the raising and lowering operators. We next review a new method for obtaining the coherent states for arbitrary potentials, it being based on the classical motion of a particle. We apply this method to the Morse oscillator. After demonstrating that in the appropriate limit our results reduce to those for the harmonic oscillator, we obtain analytic insights into published numerical results on uncertainty products for Morse-oscillator wave packets.
The comprehensive conditions concerning the harmonic limit of the Morse oscillator are investigated in this paper. These conditions extend the over-simple “classical” condition, which results by truncating the expansion of the Morse potential function in the power series of the coordinate close to the equilibrium position. The validity of the obtained results is tested by calculating the harmonic limit of the expected values of some characteristic physical observables of the Morse oscillator systems.