Related papers: Quaternionic particle in a relativistic box
We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac…
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex…
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…
A Gedanken experiment is described to explore a counter-intuitive property of quantum mechanics. A particle is placed in a one-dimensional infinite well. The barrier on one side of the well is suddenly removed and the chamber dramatically…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…
In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The…
We solve the infinite potential well problem using the methods of Heisenberg's matrix mechanics. In addition to being of educational value, the matrix mechanics allows us to deal with various unphysical issues caused by this potential in a…
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
We examine the classical problem of an infinite square well by considering Hamilton's equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac…
If $\Psi$ is a quaternionic wave function, then $i\Psi\neq \Psi i$. Thus, there are two versions of the quaternionic Schr\"odinger equation (QSE). In this article, we present the second possibility for solving the QSE, following on from a…
A quaternionic version of Quantum Mechanics is constructed using the Schwinger's formulation based on measurements and a Variational Principle. Commutation relations and evolution equations are provided, and the results are compared with…