相关论文: Quaternionic Wave Packets
The emission of gravitational waves from a system of massive objects interacting on elliptical, hyperbolic and parabolic orbits is studied in the quadrupole approximation. Analytical expressions are then derived for the gravitational wave…
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…
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case,…
One of the most puzzling consequences of interpreting quantum mechanics in terms of concepts borrowed from classical physics, is the so-called wave-particle duality. Usually, wave-particle duality is illustrated in terms of complementarity…
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…
Wave guides for classical electromagnetic fields can realize the quantum evolution of the wave function for a system of qubits. Phase shifts, switches and beam splits allow for the construction of arbitrary quantum gates. They can act at…
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a…
The complete description of neutrino oscillations require the wave packet treatment. For terrestrial experiments the contribution from the interaction of neutrino with the Earth matter would modify oscillation pattern, i.e., the dependence…
Generalization of Gaussian trial wave functions in quantum molecular dynamics models is introduced, which allows for long-range correlations characteristic for composite nuclear fragments. We demonstrate a significant improvement in the…
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows…
We address the time evolution of two- and three-dimensional nonrelativistic Gaussian wave packets in the presence of a weak external potential of arbitrary functional form. The focus of our study is the phenomenon of rotation of a Gaussian…
We present a theoretical framework that describes a wave packet of light prepared in a state of definite photon number interacting with an arbitrary quantum system (e.g. a quantum harmonic oscillator or a multi-level atom). Within this…
In this paper we investigate the gravitational waves emission by stellar dynamical structures as complex systems in the quadrupole approximation considering bounded and unbounded orbits. Precisely, after deriving analytical expressions for…
We revisit the formulation of quantum mechanics over the quaternions and investigate the dynamical structure within this framework. Similar to standard complex quantum mechanics, time evolution is then mediated by a unitary operator which…
The time evolution of wave packets in a harmonic oscillator potential is studied. Some new results for the most general case are obtained. A natural number, called ``degree of rigidity'', is introduced to describe qualitatively how much the…
An exact solution of the homogeneous wave equation, which was found previously, is treated from the point of view of continuous wavelet analysis (CWA). If time is a fixed parameter, the solution represents a new multidimensional mother…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
It is shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations. In our approach the particle mass and…
The emission of gravitational waves from a system of massive objects interacting on hyperbolic orbits is studied in the quadrupole approximation. Analytic expressions are derived for the gravitational radiation luminosity, the total energy…
As the rapidly evolving field of machine learning continues to produce incredibly useful tools and models, the potential for quantum computing to provide speed up for machine learning algorithms is becoming increasingly desirable. In…