Time evolution in the Morse potential using supersymmetry: Dissociation of the NO molecule

Abstract

We present an algebraic method for treating molecular vibrations in the Morse potential perturbed by an external laser field. By the help of a complete and normalizable basis we transform the Schrödinger equation into a system of coupled ordinary differential equations. We apply our method to calculate the dissociation probability of the NO molecule excited by chirped laser pulses. The dependence of the molecular dipole-moment on the interatomic separation is determined by a quantum-chemical method, and the corresponding transition dipole moments are given by approximate analytic expressions. These turn out to be very small between neighboring stationary states around the vibrational quantum number m = 42, therefore we propose to use additional pulses in order to skip this trapping state, and to obtain a reasonable dissociation probability.

Systematic calculation of molecular vibrational spectra through a complete Morse expansion

“…This same set was introduced in Ref. [29], on the basis of considerations related to SUSY quantum mechanics, and was applied to the context of molecular spectra in Refs. [30,31].…”

“…Following Ref. 29, we refer to |ϕ〉 as quasi‐number state. Formally, these functions resemble Morse bound states (4).…”

“…(21) with q = s , and the formal analogy with harmonic oscillator algebra is evident. Define |Ψ〉 as the only state annihilated by $\hat{A}$ ( q ): $\hat{v}$ ( q )|Ψ〉 = 0 29. For q = s , |Ψ〉 coincides with the ground state of Morse Hamiltonian, Eq.…”

Decoherence of wave packets in an anharmonic oscillator

“…Let us note that the construction given in [29] would allow us to use arbitrary initial states, but for our current purpose it suffices to consider states |x 0 , p 0 with negligible dissociation probability, i.e., coherent states that practically can be expanded in terms of the bound states |φ n , n = 0, 1, . .…”

Sub-Planck-scale structures in a vibrating molecule in the presence of decoherence

“…where x = r/r 0 − 1, r 0 is the equilibrium value of the inter-nuclear distance r and β is a range parameter. D is the dissociation energy, which has been extensively studied in a wider context of this model [37,38]. Defining λ = 2µDr 2 0 β 2 2 and s = −…”