Ladder operators for the Morse potential

Abstract

ABSTRACT:A realization of the raising and lowering operators for the Morse potential is presented. It is shown that these operators satisfy the commutation relations for the SU(2) group. Closed analytical expressions are obtained for the matrix elements of different operators such as 1/y and d/dy. The harmonic limit of the SU(2) operators is also studied and an approach previously proposed to calculate the Franck-Condon factors is discussed.

The rotating Morse potential model for diatomic molecules in the tridiagonalJ-matrix representation: I. Bound states

“…The same conclusion is reached for the CO molecule where a wider plateau of λ shows up in the oscillator basis between 5 and 16 with N = 200. Thus, it is clear that the oscillator basis is more suitable for HCl and CO molecules whereas the Laguerre basis is more suitable for H 2 and HCl. Table 2b shows the numerically generated bound states for HCl and CO using the oscillator basis as compared to the exact values generated by the analytic formula (3.8).…”

The construction of ladder operators and coherent states for the Wei Hua anharmonic oscillator using the supersymmetric quantum mechanics

“…In this paper the ladder operators for the four-parameter Wei Hua potential have been constructed by a simple algebraic procedure developed by Dong et al [17]. These operators have been obtained directly from the analytical eigenfunctions of the Schrödinger equation for the Wei Hua anharmonic oscillator.…”

“…Recently, Dong et al have derived the raising and lowering operators for the Morse [16] and Pöschl-Teller potentials [17] employing some properties of the associated Laguerre and Legandre polynomials. These operators satisfy the commutation relation for the SU(2) group.…”

“…In our study we apply the Dong et al [17] method, whereas in comparison with the study by Molski [33] in this work we have applied the standard quantum version of SUSY (so-called SUSYQM) to derive the coherent states. The work is organized as follows.…”

“…The work is organized as follows. In the second section based on the Dong et al method [17] we derive ladder operators from the analytical wave functions of the Wei Hua oscillator. In the third section, this method is extended to include the rotating oscillator with nonzero angular momentum.…”