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Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 02/2011, Volume 44, Issue 7, pp. 072001 - 9
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex... 
SPACE | SYMMETRY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUATERNIONIC QUANTUM-MECHANICS | Equivalence | Quaternions | Analogue | Mathematical analysis | Quantum mechanics | Reflection | Quantum theory | Invariants
Journal Article
Quantum Studies: Mathematics and Foundations, ISSN 2196-5609, 6/2018, Volume 5, Issue 2, pp. 357 - 390
Due to the existence of incompatible observables, the propositional calculus of a quantum system does not form a Boolean algebra, but an orthomodular lattice.... 
History and Philosophical Foundations of Physics | Quaternionic quantum systems | Mathematical Physics | Quaternionic quantum mechanics | Theoretical, Mathematical and Computational Physics | Mathematics | Quantum Physics | Quaternionic hilbert space | Quaternionic operators
Journal Article
Computer Physics Communications, ISSN 0010-4655, 2008, Volume 178, Issue 11, pp. 795 - 799
In the study of theory and numerical computations of quaternionic quantum mechanics and quantum chemistry, one of the most important tasks is to solve the... 
Least Squares eigenproblem | Quaternion matrix | Quaternionic quantum mechanics | Schrödinger equation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | FIELD THEORY | quaternion matrix | PHYSICS, MATHEMATICAL | quaternionic quantum mechanics | least squares eigenproblem
Journal Article
Advances in Applied Clifford Algebras, ISSN 0188-7009, 3/2016, Volume 26, Issue 1, pp. 169 - 182
Journal Article
Reviews in Mathematical Physics, ISSN 0129-055X, 07/2017, Volume 29, Issue 6, p. 1750021
As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda–Maeda and other authors), from the... 
real spectral analysis | von Neumann algebras | representation theory | lattice theory | Poincaré group | quaternionic quantum mechanics | Real quantum mechanics | QUANTIQUE | Poincare group | PHYSICS, MATHEMATICAL
Journal Article
Reviews in Mathematical Physics, ISSN 0129-055X, 11/2017, Volume 29, Issue 10, p. 1750034
The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann’s foundational works in the thirties. The... 
quaternionic PVMs | Quaternionic functional analysis | quaternionic spectral theorem for normal unbounded operators | quantum mechanics in quaternionic Hilbert space | THEOREM | QUANTIQUE | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | UNITARY OPERATORS
Journal Article
Reviews in Mathematical Physics, ISSN 0129-055X, 05/2019, Volume 31, Issue 4, p. 1950013
As earlier conjectured by several authors and much later established by Solèr, from the lattice-theory point of view, Quantum Mechanics may be formulated in... 
representation theory | Foundation of quantum mechanics | spectral theory | quaternionic functional analysis | PHYSICS, MATHEMATICAL
Journal Article
Advances in Applied Clifford Algebras, ISSN 0188-7009, 10/2010, Volume 20, Issue 3, pp. 745 - 763
A quaternionic version of Quantum Mechanics is constructed using the Schwinger’s formulation based on measurements and a Variational Principle. Commutation... 
variational principle | Mathematical Methods in Physics | Quaternionic quantum mechanics | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics, general | Physics | Variational principle | MATHEMATICS, APPLIED | FIELD | SCHWINGER ACTION PRINCIPLE | PHYSICS, MATHEMATICAL | GEOMETRY
Journal Article
THEORETICAL AND MATHEMATICAL PHYSICS, ISSN 0040-5779, 07/2009, Volume 160, Issue 1, pp. 1006 - 1013
The density operators obtained by taking partial traces represent improper mixtures of subsystems of a compound physical system because the coefficients in the... 
improper mixture | subentity problem | proper mixture | PHYSICS, MULTIDISCIPLINARY | HIDDEN VARIABLES | semantic realism | POSITIVE MAPS | PHYSICS, MATHEMATICAL | quaternionic quantum mechanics
Journal Article
Indian Journal of Physics, ISSN 0973-1458, 10/2017, Volume 91, Issue 10, pp. 1205 - 1209
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 05/2017, Volume 73, Issue 10, pp. 2208 - 2220
The solution of a linear quaternionic least squares (QLS) problem can be transformed into that of a linear least squares (LS) problem with JRS-symmetric real... 
Quaternionic quantum theory | Real representation | LSQR | Least squares problem | Structured preconditioner | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | EQUATIONS | ALGEBRAIC-METHOD | CONJUGATE-GRADIENT | Quantum theory | Algorithms | Information storage and retrieval | Mineral industry | Rock mechanics | Mining industry
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 02/2016, Volume 52, pp. 58 - 63
The total least squares (TLS) is a method of fitting that is appropriate when there are errors in both the observation vector b=bm×1 and the data matrix... 
Quaternionic quantum theory | Total least squares | Real representation | Quaternion total least squares | MATHEMATICS, APPLIED | MECHANICS | Analysis | Quantum theory | Methods
Journal Article
Reviews in Mathematical Physics, ISSN 0129-055X, 05/2013, Volume 25, Issue 4, p. 1350006
Journal Article
Computer Physics Communications, ISSN 0010-4655, 2007, Volume 176, Issue 7, pp. 481 - 485
Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations A X ≈ B that is appropriate when there is... 
Quaternionic quantum theory | Quaternion matrix | Algorithm | Least squares | MECHANICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | least squares | MATRICES | quaternionic quantum theory | FIELD THEORY | quaternion matrix | PHYSICS, MATHEMATICAL | algorithm | Analysis | Algorithms
Journal Article
Computer Physics Communications, ISSN 0010-4655, 2008, Volume 179, Issue 4, pp. 203 - 207
Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations A X B = E that is appropriate when there... 
Quaternionic quantum theory | Iterative algorithm | Quaternion matrix | LSQR | Least squares problem | MECHANICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | quaternionic quantum theory | quaternion matrix | least squares problem | PHYSICS, MATHEMATICAL | iterative algorithm | Quantum theory | Algorithms
Journal Article
International Journal of Theoretical Physics, ISSN 0020-7748, 5/2003, Volume 42, Issue 5, pp. 1053 - 1057
The generalization of geometric phase for the quantum systems described by quaternionic quantum mechanics is given. The geometry of the quantum cyclic... 
Mathematical and Computational Physics | Berry phase | Quantum Physics | Physics, general | Physics | holonomy | quaternionic quantum mechanics | Elementary Particles, Quantum Field Theory | Holonomy | Quaternionic quantum mechanics | PHYSICS, MULTIDISCIPLINARY | GEOMETRIC PHASE
Journal Article
Foundations of Physics, ISSN 0015-9018, 5/2013, Volume 43, Issue 5, pp. 656 - 664
Journal Article
Optik, ISSN 0030-4026, 05/2019, Volume 184, pp. 499 - 507
Employing the quaternionic fundamental commutator bracket between position and momentum and the electromagnetic quaternion as a wavefunction, we have found new... 
Quantized Maxwell's | Quantum mechanics | Angular momentum | Axioic field | Photon | Quaternionic Maxwell's equations | Matter field interaction | ANGULAR-MOMENTUM | OPTICS
Journal Article
International Journal of Theoretical Physics, ISSN 0020-7748, 1/2013, Volume 52, Issue 1, pp. 279 - 292
Journal Article
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