An-Najah University Journal for Research - A (Natural Sciences)

The Wave Equation with Energy Dependent Potential - the Linear Case
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Article info

2010-10-06
2011-03-09
2011-03-09
49 - 62

Keywords

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.

Recommended Citation

Lombard, R. (2011). The Wave Equation with Energy Dependent Potential - the Linear Case. An-Najah University Journal for Research - A (Natural Sciences), 25(1), 49–62. https://doi.org/10.35552/anujr.a.25.1.141
[1]R. Lombard, “The Wave Equation with Energy Dependent Potential - the Linear Case,” An-Najah University Journal for Research - A (Natural Sciences), vol. 25, no. 1, pp. 49–62, Mar. 2011, doi: 10.35552/anujr.a.25.1.141.
Lombard, Ronald. “The Wave Equation with Energy Dependent Potential - the Linear Case.” An-Najah University Journal for Research - A (Natural Sciences), vol. 25, no. 1, Mar. 2011, pp. 49–62. Crossref, https://doi.org/10.35552/anujr.a.25.1.141.
1.Lombard R. The Wave Equation with Energy Dependent Potential - the Linear Case. An-Najah University Journal for Research - A (Natural Sciences) [Internet]. 2011 Mar;25(1):49–62. Available from: http://dx.doi.org/10.35552/anujr.a.25.1.141
Lombard, Ronald. “The Wave Equation with Energy Dependent Potential - the Linear Case.” An-Najah University Journal for Research - A (Natural Sciences) 25, no. 1 (March 2011): 49–62. https://doi.org/10.35552/anujr.a.25.1.141.

The Wave Equation with Energy Dependent Potential - the Linear Case
المؤلفون:

معلومات المقال

2010-10-06
2011-03-09
2011-03-09
49 - 62

الكلمات الإفتتاحية

الملخص

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.

Recommended Citation

Lombard, R. (2011). The Wave Equation with Energy Dependent Potential - the Linear Case. An-Najah University Journal for Research - A (Natural Sciences), 25(1), 49–62. https://doi.org/10.35552/anujr.a.25.1.141
[1]R. Lombard, “The Wave Equation with Energy Dependent Potential - the Linear Case,” An-Najah University Journal for Research - A (Natural Sciences), vol. 25, no. 1, pp. 49–62, Mar. 2011, doi: 10.35552/anujr.a.25.1.141.
Lombard, Ronald. “The Wave Equation with Energy Dependent Potential - the Linear Case.” An-Najah University Journal for Research - A (Natural Sciences), vol. 25, no. 1, Mar. 2011, pp. 49–62. Crossref, https://doi.org/10.35552/anujr.a.25.1.141.
1.Lombard R. The Wave Equation with Energy Dependent Potential - the Linear Case. An-Najah University Journal for Research - A (Natural Sciences) [Internet]. 2011 Mar;25(1):49–62. Available from: http://dx.doi.org/10.35552/anujr.a.25.1.141
Lombard, Ronald. “The Wave Equation with Energy Dependent Potential - the Linear Case.” An-Najah University Journal for Research - A (Natural Sciences) 25, no. 1 (March 2011): 49–62. https://doi.org/10.35552/anujr.a.25.1.141.

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