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

Abstract

The unknown ladder operators for the Wei Hua potential have been derived within the algebraic approach. The method is extended to include the rotating oscillator. The annihilation and creation operators have been obtained with the use of the factorization method. The coherent states for the Wei Hua anharmonic oscillator, which are eigenstates of the annihilation operator and minimize the generalized position-momentum uncertainty relation, are constructed in the framework of the supersymmetric quantum mechanics. The constructed ladder operators can be applied to compute the matrix elements in theoretical spectroscopy due to the fact that this potential is widely used to a proper description the large-amplitude vibrations of diatomic molecules.

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

“…Therefore, they satisfy the two fundamental requirements established for the coherent states of an anharmonic oscillator. Some similar minimum-uncertainty coherent states have been recently derived algebraically by Molski [38] and Mikulski et al [39].…”

Complete non-relativistic bound state solutions of the Tietz-Wei potential via the path integral approach

“…In this paper, we have seen that the problem of the Tietz-Wei potential is completely solved in the context of Feynman's path integrals, contrary to the naive attempts of its treatment by various techniques [6,7,[9][10][11][12][13] leading to partially acceptable results. It should be noted that a suitable study of this potential requires distinguishing three cases representing the standard Manning-Rosen potential for e −b h re ≤ c h < 1, the defined Manning-Rosen potential in a half-space when 0 < c h < e −b h re and the Rosen-Morse potential for −1 < c h < 0.…”

“…The approximate analytical solutions of the Schrödinger, Klein-Gordon and Dirac equations were also proposed by adopting the Pekeris approximation [8] and by applying three types of techniques namely the asymptotic iteration method, the functional analysis approach and the supersymmetry in quantum mechanics [9]. In another study, the construction of Ladder operators by the algebraic approach and coherent states in the context of supersymmetry in quantum mechanics for the Tietz-Wei anharmonic potential was discussed [10]. The method based on the appropriate quantization rule has recently been applied to determine the energy spectrum of a set of diatomic molecules in the presence of the Tietz-Wei potential [11] and the modified Tietz-Wei potential [12].…”