The Morse oscillator under time-dependent external fields

Abstract

A method to solve the equations for the Morse oscillator under intense time-dependent external fields is presented. Exact analytical formulas for the dipole matrix elements are calculated by the use of the hypergeometric algebra. The continuum is described by an expansion using Laguerre functions. The full algorithm for the calculation of wave functions can be controlled by the convergence of series and by the errors of a first order integration method. We apply our technique to the selective preparation of high overtones by femtosecond laser pulses. The population of the target state is optimized as a function of the intensity and frequency. Introducing a second simultaneous laser, we study the effects of relative frequency and phase over the target state population and dissociation channels. The calculations exhibit a rich interference pattern showing the enhancement and the suppression of the target population by varying the laser parameters.

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

“…The spectrum is defined in such a way that states with negative energy are bound and states with zero or positive energy are unbound. For a discussion on the unbound states and spectrum, see, for example [36][37][38]. The bound state conditions imply that the quantum numbers n, m may take the following values [39] n, m ∈ {0, 1, .…”

“…We remark that the state | p is only an approximate eigenstate of B − because the term proportional to |ν max does not appear in the expansion (36), we add it in by hand. This is a general feature of ladder operator eigenstate definitions of coherent states with finite spectra.…”

Quantum work distribution for a driven diatomic molecule

“…The time-independent Morse oscillator can be solved exactly [36]. For energies less than zero the solution corresponds to bound states, which can be expressed as [38]…”

“…In contrast to the bound state the scattering states correspond to a continuous part of the spectrum, which is characterized by the positive and real quantum number κ. This quantum number can be associated with the momentum, p = κ, and the eigenenergies become accordingly, In complete analogy to the bound states also the scattering states can be expressed in terms of Laguerre polynomials [38]. In Fig.…”

Optimal laser control of molecular photoassociation along with vibrational stabilization

“…Analytical expressions for the dipole moment matrix elements fl mm 0 ; l mm and l mm 0 g are available for a variety of functional forms of lðrÞ [22][23][24].…”