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Paper   IPM / Physic / 7616
School of Physics
  Title:   Supersymmetry Approaches to the Radial Bound States of the Hydrogen-like Atoms
1.  A. Chenaghlou
2.  H. Fakhri
  Status:   Published
  Journal: Int J. Quantum Chem
  No.:  3
  Vol.:  101
  Year:  2005
  Pages:   291-304
  Supported by:  IPM
Introducing the associated Bessel polynomials in terms of two non-negative integers, we factorize their corresponding differential equation into a product of first order differential operators by four different ways as shape invariance equations. Then, the radial part of the bound states of the Schrödinger equation of a hydrogen-like atom is derived by using one of the factorization methods in the framework of supersymmetric quantum mechanics. In this approach, we regenerate the radial bound states and their corresponding spectrum, which are consistent with the well-known facts. Based on the generalization of supersymmetry idea, we shall show that two Hydrogen-like atoms with the same energy for the electron possess three extra supersymmetric structures in addition to an ordinary one.

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