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Energy-dependent potentials and the problem of the equivalent local potential
Yekken R., J. Lombard R.
Journal of Physics A Mathematical and Theoretical 43 (2010) 125301 - http://hal.in2p3.fr/in2p3-00464576
Mathématiques/Physique mathématique
Physique/Physique mathématique
Energy-dependent potentials and the problem of the equivalent local potential
R. Yekken, R. J. Lombard1
1 :  IPNO - Institut de Physique Nucléaire d'Orsay
http://ipnweb.in2p3.fr
CNRS : UMR8608 – IN2P3 – Université Paris XI - Paris Sud
IPN - 15, rue Georges Clemenceau - 91406 ORSAY CEDEX
France
The properties of the wave equation are studied in the case of energy-dependent potentials for bound sates. The nonlinearity induced by the energy dependence requires modification of the standard rules of quantum mechanics. These modifications are briefly recalled. Analytical and numerical solutions are given in the three-dimensional space for power-law radial shape potentials with a linear energy dependence. This last is chosen since it allows the construction of a coherent theory. Among the results, we stress the saturation of the spectrum observed for confining potentials: as the quantum numbers increase, the eigenvalues reach an upper limit. Finally, the problem of the equivalent local potential is discussed. The existence of analytical solutions presents a good opportunity to tackle this problem in detail.

Articles dans des revues avec comité de lecture
2010
Journal of Physics A Mathematical and Theoretical
43
125301

Mathematical physics – Quantum information and quantum mechanics