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arXiv:hep-th/0111143 · Journal of Physics A Mathematical and General

Quaternionic potentials in non-relativistic quantum mechanics

Stefano De Leo, Gisele Cristina Ducati, C. C. Nishi

Published Jun 21, 2002• 70 citations
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Abstract

We discuss the Schrödinger equation in the presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to investigate an underlying quaternionic quantum dynamics in particle physics. Experimental tests and proposals to observe quaternionic quantum effects by neutron interferometry are briefly reviewed.

DOI
10.1088/0305-4470/35/26/305

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We discuss the Schrödinger equation in the presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to investigate an underlying quaternionic quantum dynamics in particle physics. Experimental tests and proposals to observe quaternionic quantum effects by neutron interferometry are briefly reviewed.
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Abstract In this final chapter we turn to issues relating to the role of quaternionic quantum mechanics in physics and to its future development. In the first section, we speculate on the possibility that a new level of physical structure, in which quaternionic quantum field theory plays an essential role, lies near the Planck scale, with the observed physics of the standard model a CC( 1,1) asymptotic dynamics. In the second section, we discuss both experimental tests for residual quaternionic effects and the implications of quaternionic quantum mechanics for conceptual questions in quantum measurement theory. In the third section, we summarize a number of open questions, many already noted earlier in the text, that point to future directions for development of the theory.
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The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the possibility of self-interacting physical systems. The self-interaction precludes confining states, and also imposes non-stationary quantum states, both of them representing novel situations that cannot be observed in terms of quantum wave functions. These results remark the differences between quaternionic quantum mechanics ($\mathbbm H$QM) and complex quantum mechanics ($\mathbbm C$QM), and also establish a method of solving the wave equation that may be applied to a variety of different cases.