An alternative simple solution of the sextic anharmonic oscillator and perturbed coulomb problems


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IKHDAİR S., Sever R.

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, vol.18, no.10, pp.1571-1581, 2007 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 10
  • Publication Date: 2007
  • Doi Number: 10.1142/s0129183107011583
  • Journal Name: INTERNATIONAL JOURNAL OF MODERN PHYSICS C
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1571-1581
  • Keywords: sextic anharmonic oscillator problem, perturbed Coulomb problem, bound states, wave functions, Schrodinger equation, SUPERSYMMETRIC QUANTUM-MECHANICS, HILL DETERMINANT METHOD, BOUND-STATES, ENERGY-LEVELS, POTENTIALS

Abstract

Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic an-harmonic oscillator and confining perturbed Coulomb models in D-dimensions. We show that the perturbed Coulomb problem with eigenvalue E can be transformed to a sextic anharmonic oscillator problem with eigenvalue P. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solutions of these potentials exist when their coupling parameters with k = D + 2l appearing in the wave equation satisfy certain constraints.