“School of Physics”
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| Paper IPM / P / 7616 |
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| Abstract: | |||||
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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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