Eigenstates, coherent states, and uncertainty products for the Morse oscillator

TLDR: In this article, the exact, normalized, closed-form eigenfunctions for the one-dimensional Morse oscillator, as well as the raising and lowering operators, were obtained based on the classical motion of a particle.

Abstract: 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.