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A pseudo Coulombian potential in D=1 dimensional space

Abstract : In the D=1 dimensional space, we study the bound state solutions of the potential V(x) = -\frac{e}{x} + \frac{b}{x^2} (e, b>0). They occur on the right half-plane xin[0, ∞[. In the limit b→0, we recover the spectrum of the D=1 Coulomb potential. Supersymmetric properties are briefly discussed. The model is extended by considering complex coupling constants. Nonlinear effects are also treated by considering a linear energy dependence of the e coupling constant.
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Contributor : Sophie Heurteau <>
Submitted on : Thursday, December 10, 2009 - 2:51:40 PM
Last modification on : Wednesday, September 16, 2020 - 4:07:56 PM

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R. J. Lombard, R. Mezhoud, R. Yekken. A pseudo Coulombian potential in D=1 dimensional space. Physica Scripta, IOP Publishing, 2009, 80, 065005 (7p.). ⟨10.1088/0031-8949/80/06/065005⟩. ⟨in2p3-00440371⟩

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