Abstract
In this present study, we have employed the techniques of exact quantization rule and ansatz solution method to obtain closed form expressions for the rotational-vibrational eigensolutions of the D-dimensional Schrödinger equation for the improved Wei potential, for cases of h′ ≠ 0 and h′ = 0. By using our derived energy equation and choosing arbitrary values of n and ℓ, we have computed the bound state rotational-vibrational energies of CO, H2 and LiH for various quantum states. The mean absolute percentage deviation (MAPD) and the Lippincott criterion ware used as a goodness-of-fit indices to compare our result with the Rydberg-Klein-Rees (RKR) and improved Tietz potential data in the literature. MAPD of 0.2862%, 0.2896% and 0.0662% relative to the RKR data for CO ware obtained. For the improved Wei and Morse potential, our computed energy eigenvalues for CO, H2 and LiH are in excellent agreement with existing results in the literature
Highlights
Extensive literature review reveals that wave functions are of tremendous importance in both relativistic and nonrelativistic quantum mechanics because they completely define the quantum mechanical system under review (Yanar et al, 2020; Hamzavi et al, 2012), information such as energy of the system, momentum, frequency of vibration, speed and wavelength are readily obtainable if the wave function of the system is known (Eyube et al, 2019a)
We aimed at obtaining closed form expressions for the rotational-vibrational eigensolutions of the D-dimensional Schrödinger equation for the improved Wei potential via exact quantization rule (EQR) and ansatz solution method
THEORETICAL APPROACH Overview of the concepts of exact quantization rule Here we present in outline form, the basic concepts of EQR, a detailed description of the concept is given by Ma and Xu (2005)
Summary
THEORETICAL APPROACH Overview of the concepts of exact quantization rule Here we present in outline form, the basic concepts of EQR, a detailed description of the concept is given by Ma and Xu (2005). The EQR has been proposed to solve the onedimensional Schrödinger equation given by:. The first term, Nπ, is the contribution from the nodes of the wave function, and the second term is referred to as the quantum correction. N r is the radial wave function, r is the internuclear separation and Veff r is the effective potential defined in terms of a spherically symmetric potential V r and a parameter Λ by: Veff r V r. The parameters h (dimensionless) and b (in m-1) are determined through f2 and f3 the second and third derivatives of the potential energy function (Eq (14)) at r re respectively (Jia et al, 2012), by using the following relationship d 2 V r f2. Employing the relationship between the vibrational-rotational coupling constant, e and f3 (Jia et al, 2012), viz: e
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