Title: On a connection between radial Schrödinger equations for different power-law potentials
Abstract: A general correspondence is given between the radial Schrödinger equations (in arbitrary dimensions) for confining- and inverse-power law potentials. The wave functions and Green’s functions of the two types of potentials are shown to differ by little more than a change of variable (a special case being the well-known equivalence of the harmonic oscillator and Coulomb problems). This gives rise to relationships between the discrete state eigenvalues and matrix elements. Following the lines of a recent paper by Gazeau, the relevance of this correspondence to Sturmian representations for power law potentials is examined. Generalizations are considered for potentials containing a linear combination of powers of r.
Publication Year: 1980
Publication Date: 1980-11-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 27
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