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Solutions of the Schrödinger equation in the tridiagonal representation with the noncentral electric dipole plus a novel angle-dependent component

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Abstract

A noncentral ring-shaped potential is proposed in which the noncentral electric dipole and a novel angle-dependent component are included, the radial part is selected as the Coulomb potential or the harmonic oscillator potential. The exact solution of the Schrödinger equation with this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relation for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre polynomials. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation.

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Authors and Affiliations

  1. Department of Physics and Electronic Engineering, Weinan Teachers University, Weinan, 714000, People’s Republic of China

    Guo-Qing Huang-Fu

  2. College of Physics and Information Technology, Shaanxi Normal University, Xi’an, 710062, People’s Republic of China

    Min-Cang Zhang

Authors
  1. Guo-Qing Huang-Fu
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  2. Min-Cang Zhang
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Correspondence to Min-Cang Zhang.

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Huang-Fu, GQ., Zhang, MC. Solutions of the Schrödinger equation in the tridiagonal representation with the noncentral electric dipole plus a novel angle-dependent component. J Math Chem 50, 1988–2000 (2012). https://doi.org/10.1007/s10910-012-0015-9

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  • DOI: https://doi.org/10.1007/s10910-012-0015-9

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