Quaternionic bound states

Details Quaternionic bound states Quaternionic bound states

2005-04-07

arxiv.org/abs/math-ph/0504025v1

Journal of Physics A 38, 3443-3454 (2005)

Physics

Mathematical Physics

11 pages, AMS-TeX, 2 figures

Scientific paper

We study the bound-state solutions of vanishing angular momentum in a quaternionic spherical square-well potential of finite depth. As in the standard quantum mechanics, such solutions occur for discrete values of energies. At first glance, it seems that the continuity conditions impose a very restrictive constraint on the energy eigenvalues and, consequently, no bound states was 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 it is the analysis of confined wave packets and tunnelling times in this new formulation of quantum theory.

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