Vibrational coherent states for Morse oscillator

Parametric-time coherent states for Morse potential

“…× (λ + ) (z+i|m|+im) (λ − ) (n r +i|m|−im) √ (n r + i |m| + im + 1) (z + i |m| − im + 1) |z, im (27) where |z, im are the two-dimensional oscillator states defined in (21) and the contour C in the complex z-plane comes from −∞ − i to +∞ + i . Equation (27) shows that when p 0 > 0 the evolution factor (the argument of the exponential) becomes complex.…”

“…Equation (27) shows that when p 0 > 0 the evolution factor (the argument of the exponential) becomes complex. For this reason the trigonometric functions in (25) and (26) become hyperbolic functions and the dispersions increase (decrease) for the outgoing (incoming) waves.…”

“…The kernel of this problem is obtained by transforming it into a radial harmonic oscillator in parametric time [19,20]. The Morse-potential problem has SO(2,1) dynamical symmetry and the coherent states for this problem are discussed by using group theoretical methods [21][22][23] and algebraic methods [24][25][26][27].…”

Application of the anharmonic coherent states to the vibronic interaction

“…The coherent states as eigenstates of the annihilation operator of the harmonic oscillator (Glauber states) and the coherent states obtained by applying the displacement operator on the vacuum state have many applications in physics [1]. The coherent states for the harmonic oscillator were extended to anharmonic vibrations, particularly to the Morse oscillator [2].…”

“…The vibronic coupling between degenerate electronic states and degenerate vibrations of a physical system (molecules, crystals) with octahedral symmetry has been explored using for the vibrations the classical wavefunctions of the harmonic oscillator [3], and also coherent states [4,5]. Recently we have been built the anharmonic coherent states [2] and we used them to study vibronic interaction E ⊗ ε [6] and T ⊗ ε [7] coupling.…”