Stefano De Leo and Gisele C Ducati 2005 J. Phys. A: Math. Gen. 38 3443 doi:10.1088/0305-4470/38/15/014
Quaternionic bound states
Stefano De Leo1 and Gisele C Ducati2
Show affiliationsWe study the bound-state solutions of vanishing angular momentum in a quaternionic spherical square-well potential of finite depth. As in standard quantum mechanics, such solutions occur for discrete values of energy. At first glance, it seems that the continuity conditions impose a very restrictive constraint on the energy eigenvalues and, consequently, no bound states were expected for energy values below the pure quaternionic potential. Nevertheless, a careful analysis shows that pure quaternionic potentials do not remove bound states. It is also interesting to compare these new solutions with the bound state solutions of the trial-complex potential. The study presented in this paper represents a preliminary step towards a full understanding of the role that quaternionic potentials could play in quantum mechanics. Of particular interest for the authors is the analysis of confined wave packets and tunnelling times in this new formulation of quantum theory.
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Issue 15 (15 April 2005)
Received 13 October 2004, in final form 25 February 2005
Published 30 March 2005
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Quaternionic bound states
Stefano De Leo and Gisele C Ducati 2005 J. Phys. A: Math. Gen. 38 3443
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