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Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

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Abstract

For arbitrary values n and ℓ quantum numbers, we present the solutions of the 3-dimensional Schrödinger wave equation with the pseudoharmonic potential via the SU(1, 1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The matrix elements r 2 and \({r\frac{d}{dr}}\) are obtained (in a closed form) directly from the creation and annihilation operators. In addition, by applying the Hellmann–Feynman theorem, the expectation values of r 2 and p 2 are obtained. The energy states, the expectation values of r 2 and p 2 and the Heisenberg uncertainty products (HUP) for set of diatomic molecules (CO, NO, O2, N2, CH, H2, ScH) for arbitrary values of n and ℓ quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature. It is also shown that the HUP is obeyed for all diatomic molecules considered.

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  1. Theoretical Physics Section, Department of Physics, University of Ilorin, P. M. B. 1515, Ilorin, Kwara state, Nigeria

    K. J. Oyewumi

  2. School of Chemistry, University of Hyderabad, Hyderabad, 50046, India

    K. J. Oyewumi & K. D. Sen

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  1. K. J. Oyewumi
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Oyewumi, K.J., Sen, K.D. Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules. J Math Chem 50, 1039–1059 (2012). https://doi.org/10.1007/s10910-011-9967-4

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