Generalized quantum isotonic nonlinear oscillator in d dimensions


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Hall R. L. , Saad N., YEŞİLTAŞ Ö.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.43, no.46, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 46
  • Publication Date: 2010
  • Doi Number: 10.1088/1751-8113/43/46/465304
  • Title of Journal : JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Abstract

We present a supersymmetric analysis for the d-dimensional Schrodinger equation with the generalized isotonic nonlinear-oscillator potential V (r) = B(2)/r(2)+omega(2)r(2)+ 2g(r(2) - a(2))/(r(2) + a(2))(2), B >= 0. We show that the eigenequation for this potential is exactly solvable provided g = 2 and (omega a(2))(2) = B(2) + (l + (d - 2)/2)(2). Under these conditions, we obtain explicit formulae for all the energies and normalized bound-state wavefunctions.