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

SPACE | SYMMETRY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUATERNIONIC QUANTUM-MECHANICS | Equivalence | Quaternions | Analogue | Mathematical analysis | Quantum mechanics | Reflection | Quantum theory | Invariants

Journal Article

Canadian Journal of Physics, ISSN 0008-4204, 2016, Volume 94, Issue 3, pp. 262 - 266

In this paper, the Schrödinger equation for quaternionic quantum mechanics with a Dirac delta potential has been investigated. The derivative discontinuity...

reflection and transmission coefficients | mécanique quantique des quaternions | 03.65.Ca | 02.30.Tb | équation de Schrödinger | coefficients de réflexion et de transmission | potentiel en fonction delta | quaternionic quantum mechanics | Schrödinger equation | Dirac delta potential | Quaternionic quantum mechanics | Reflection and transmission coefficients | Usage | Wave functions | Schrodinger equation | Scattering (Physics) | Analysis | Quantum theory | Deltas | Discontinuity | Quantum mechanics | Boundary conditions | Reflection | Schroedinger equation | Derivatives

reflection and transmission coefficients | mécanique quantique des quaternions | 03.65.Ca | 02.30.Tb | équation de Schrödinger | coefficients de réflexion et de transmission | potentiel en fonction delta | quaternionic quantum mechanics | Schrödinger equation | Dirac delta potential | Quaternionic quantum mechanics | Reflection and transmission coefficients | Usage | Wave functions | Schrodinger equation | Scattering (Physics) | Analysis | Quantum theory | Deltas | Discontinuity | Quantum mechanics | Boundary conditions | Reflection | Schroedinger equation | Derivatives

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

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

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

Quaternion least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations $${AX \approx B}$$ A X ≈ B and $${AXC...

Mathematical Methods in Physics | Quaternionic quantum mechanics | Theoretical, Mathematical and Computational Physics | Least squares | Quaternion matrices | Real representation | Applications of Mathematics | Physics, general | Physics | Complex representation | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Computer science | Quantum theory | Methods

Mathematical Methods in Physics | Quaternionic quantum mechanics | Theoretical, Mathematical and Computational Physics | Least squares | Quaternion matrices | Real representation | Applications of Mathematics | Physics, general | Physics | Complex representation | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Computer science | Quantum theory | Methods

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

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

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

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

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

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

In this article, we have studied scattering of non-relativistic particles from Quaternionic double Dirac delta potential. This scattering is investigated in...

Double dirac delta potential | Astrophysics and Astroparticles | Quaternionic quantum mechanics | Ramsauer–Townsend effect | Physics, general | Reflection and transmission coefficients | Physics | Ramsauer-Townsend effect | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | ELECTRONS | SPACES | TENSOR PRODUCT | QUANTUM-MECHANICS | OPERATORS | EQUATION | SCATTERING | Quaternions | Mathematical analysis | Scattering | Quantum mechanics | Relativistic particles | Current density | Quantum physics

Double dirac delta potential | Astrophysics and Astroparticles | Quaternionic quantum mechanics | Ramsauer–Townsend effect | Physics, general | Reflection and transmission coefficients | Physics | Ramsauer-Townsend effect | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | ELECTRONS | SPACES | TENSOR PRODUCT | QUANTUM-MECHANICS | OPERATORS | EQUATION | SCATTERING | Quaternions | Mathematical analysis | Scattering | Quantum mechanics | Relativistic particles | Current density | Quantum physics

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

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

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

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical...

Slice regular functions | Operator algebras | Spectral theory | Non-commutative functional calculus | Quaternionic quantum mechanics | Continuous functional calculus C | algebras | Quaternionic Hilbert space | slice regular functions | spectral theory | C-algebras | QUANTIQUE | REGULAR FUNCTIONS | PHYSICS, MATHEMATICAL | non-commutative functional calculus | continuous functional calculus | ALGEBRAS | operator algebras | QUANTUM-MECHANICS | quaternionic quantum mechanics

Slice regular functions | Operator algebras | Spectral theory | Non-commutative functional calculus | Quaternionic quantum mechanics | Continuous functional calculus C | algebras | Quaternionic Hilbert space | slice regular functions | spectral theory | C-algebras | QUANTIQUE | REGULAR FUNCTIONS | PHYSICS, MATHEMATICAL | non-commutative functional calculus | continuous functional calculus | ALGEBRAS | operator algebras | QUANTUM-MECHANICS | quaternionic quantum mechanics

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

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

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

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

We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on...

Philosophy of Science | Born rule | Quantum Physics | Quantum foundations | Statistical Physics, Dynamical Systems and Complexity | Physics | History and Philosophical Foundations of Physics | Quaternions | Quaternionic POVMs | Quaternionic quantum channels | Mechanics | Division rings | Classical and Quantum Gravitation, Relativity Theory | MECHANICS | GLEASON | PHYSICS, MULTIDISCIPLINARY | THEOREM | Hilbert space | Research | Quantum theory | Mathematical physics | Physics - Quantum Physics

Philosophy of Science | Born rule | Quantum Physics | Quantum foundations | Statistical Physics, Dynamical Systems and Complexity | Physics | History and Philosophical Foundations of Physics | Quaternions | Quaternionic POVMs | Quaternionic quantum channels | Mechanics | Division rings | Classical and Quantum Gravitation, Relativity Theory | MECHANICS | GLEASON | PHYSICS, MULTIDISCIPLINARY | THEOREM | Hilbert space | Research | Quantum theory | Mathematical physics | Physics - Quantum Physics

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

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

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order...

Quaternionic quantum mechanics | Theoretical, Mathematical and Computational Physics | Klein-Gordon equation | Higher spin | Quantum Physics | Clifford algebra | Physics, general | Mott scattering | Physics | Elementary Particles, Quantum Field Theory | FIELDS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | HYPERBOLIC NUMBERS | PHYSICS | QUANTUM-MECHANICS | QUANTIZATION | RELATIVITY | Analysis | Quantum theory | Electromagnetism

Quaternionic quantum mechanics | Theoretical, Mathematical and Computational Physics | Klein-Gordon equation | Higher spin | Quantum Physics | Clifford algebra | Physics, general | Mott scattering | Physics | Elementary Particles, Quantum Field Theory | FIELDS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | HYPERBOLIC NUMBERS | PHYSICS | QUANTUM-MECHANICS | QUANTIZATION | RELATIVITY | Analysis | Quantum theory | Electromagnetism

Journal Article

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