The Wave Equation with Energy Dependent Potential - the Linear Case

dc.contributor.author	Ronald Lombard
dc.date.accessioned	2016-09-07T10:16:46Z
dc.date.available	2016-09-07T10:16:46Z
dc.date.issued	2011
dc.description.abstract	We summarize recent works devoted to energy dependent potentials. It concerns the class of potentials having a coupling constant depending linearly on the energy. Introduced in the Schrödinger equation, it produces non-linear effects. Few cases admit analytical solutions. They are of great help to get acquainted with this non-linearity. The harmonic oscillator and the Coulomb potential are presented as typical examples. Applications concern heavy. quark-anti-quark systems, as well as the many-body problem with harmonic interactions. Finally, we show that the energy dependence does not modify the number of bound states of attractive potentials. It can regularize some potentials singular at the origin. For instance, the ground state energy of the -1/r2 potential in D=3 dimensional space becomes finite for finite energy dependence.	en
dc.identifier	1727-2114
dc.identifier.uri	http://hdl.handle.net/20.500.11888/1936
dc.title	The Wave Equation with Energy Dependent Potential - the Linear Case	en

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