FIZIKA B 12 (2003)  3, 201 - 218

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01 Parvis du Breuil, 92160 Antony, France

Received 25 November 2002; Accepted 8 December 2003
Online 19 April 2004

The potentials involving singularities considered in this work result from the construction starting with higher-order-generation superpotentials. The second generation with a single base as well as the third one with a double base will be discussed. According to the choice of these bases, a number of results, which may be interesting from the theoretical point of view, can be observed such as the partial breaking of the symmetry or the construction of a new type of exactly solvable potentials which show existence of eigenstates with positive eigenvalues. Extension to the third generation potential of the theorem on quasi-exact solvability will also be discussed.

PACS numbers: 03.64.Ge
UDC 530.145

Keywords: higher-order superpotentials, singularities, second generation with a single base, third generation with a double base, breaking of symmetry, existence of eigenstates

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