Franck-Condon factors for the Morse potential

Abstract

ABSTRACT:The aim of this study is to establish a new representation for the dynamic algebra of the Morse oscillator and to establish the raising and lowering operators based on the properties of the confluent hypergeometric functions.Using the representation we have obtained a recurrent analytic method for the calculus of the Franck᎐Condon factors.

Photon-added coherent states for the Morse oscillator

“…The arguments for such an increasing interest for the Morse potential generally, and for the construction of the coherent states of the Morse oscillator especially, in our opinion, are the following: (a) the Morse potential allows an analytical solution of the Schrödinger equation and is characterized by a finite number (denoted here by [N/2], where N is a constant which characterizes the potential shape of the Morse oscillator, as we can see below) of bound states (where [x] represents the integer part of x); (b) theoretical spectroscopic results obtained by using the Morse potential in the case of vibrational motion of diatomic [28] (as well as polyatomic [6,29]) molecules, and also in the case of molecular interactions, agree well with experimental spectrum [30]; (c) the systematic analysis of transition intensities and Franck-Condon factors are also possible [31,32].…”

Ladder operators for the Morse potential

“…On the other hand, we show that subsequent work using the results of Ref. 33 must be revised and, in particular, that the calculation of Franck–Condon factors through linear recurrence relations lacks generality and can only be used in very particular cases.…”

“…Recently, Avram and Drăgănescu 33 established a realization of the raising and lowering operators of the Morse potential, basing their approach on some properties of the confluent hypergeometric functions. They claimed that these operators, together with a number operator, satisfy the commutation relations of the SO(2,1) group and proposed an algebraic method to establish recurrence relations for the Franck–Condon factors.…”

The algebraic approach for the derivation of ladder operators and coherent states for the Goldman and Krivchenkov oscillator by the use of supersymmetric quantum mechanics

“…gȃ . nescu [22] have constructed the ladder operators for the Morse potential. They used properties of the confluent hypergeometric function in the recurrent analytic form.…”