Quaternionic potentials in non-relativistic quantum mechanics

We discuss the Schrodinger equation in 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.Comment: 21 pages, 16 figures (ps), AMS-Te

Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

Questions of quality in repositories of open educational resources: a literature review

Open educational resources (OER) are teaching and learning materials which are freely available and openly licensed. Repositories of OER (ROER) are platforms that host and facilitate access to these resources. ROER should not just be designed to store this content – in keeping with the aims of the OER movement, they should support educators in embracing open educational practices (OEP) such as searching for and retrieving content that they will reuse, adapt or modify as needed, without economic barriers or copyright restrictions. This paper reviews key literature on OER and ROER, in order to understand the roles ROER are said or supposed to fulfil in relation to furthering the aims of the OER movement. Four themes which should shape repository design are identified, and the following 10 quality indicators (QI) for ROER effectiveness are discussed: featured resources; user evaluation tools; peer review; authorship of the resources; keywords of the resources; use of standardised metadata; multilingualism of the repositories; inclusion of social media tools; specification of the creative commons license; availability of the source code or original files. These QI form the basis of a method for the evaluation of ROER initiatives which, in concert with considerations of achievability and long-term sustainability, should assist in enhancement and development. Keywords: open educational resources; open access; open educational practice; repositories; quality assuranc

Quaternionic Electroweak Theory and CKM Matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published

Representations of U(1,q) and Constructive Quaternion Tensor Products

The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the eigenvalues must be right-eigenvalues and that the only consistent scalar products are the complex ones. We also define an explicit quaternion tensor product which leads to a set of additional group representations for integer ``spin''.Comment: 28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di Lecc