Article

# Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

Department of Engineering Physics, Gaziantep University, Ayıntap, Gaziantep, Turkey

Journal of Physics A General Physics 07/2001; 34(40). DOI: 10.1088/0305-4470/34/40/305 Source: arXiv

**ABSTRACT**

The eigenvalues of the potentials

$V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4

}}{r^{4}}$ and

$V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^

{6}}$, and of the special cases of these potentials such as the Kratzer and

Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The

explicit dependence of these potentials in higher-dimensional space is

discussed, which have not been previously covered.

$V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4

}}{r^{4}}$ and

$V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^

{6}}$, and of the special cases of these potentials such as the Kratzer and

Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The

explicit dependence of these potentials in higher-dimensional space is

discussed, which have not been previously covered.

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