Related papers: On the truncation of the harmonic oscillator wavep…
The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple…
In this work, phase singularities embedded in a wavepacket are shown to act as sources of atypical localized oscillations when the packet interacts with a linear system. We refer to these oscillations as \textit{chirpons}, since they arise…
The main purpose of this paper is to demonstrate and illustrate, once again, the potency of the variational technique as an approximation procedure for the quantization of quantum mechanical systems. By choosing particle-in-a-box…
A consistent constructive covariant description of neutrino flavour transition amplitude in vacuum is presented. To this end a special generalized relativistic wave packet is constructed with correct extension onto the higher spins. This…
It is shown that harmonic functions on some subsets, subharmonic and coinciding everywhere outside of these sets, actually coincide everywhere.
We point out three apparent inconsistencies in the treatment of oscillation coherence from reactor neutrino and source neutrino experiments in recent paper "Damping of neutrino oscillations, decoherence and the lengths of neutrino wave…
A class of truncated tight-binding Hermitian and non-Hermitian lattices with commensurate energy levels, showing periodic reconstruction of the wave packet, is presented. Examples include exact Bloch oscillations on a finite lattice,…
Coupled quantum harmonic oscillators, studied by many authors using many different techniques over the decades, are frequently used toy-models to study open quantum systems. In this manuscript, we explicitly study the simplest oscillator…
We construct a complete set of eigenfunctions of the q-deformed harmonic oscillator on the quantum line. In particular the eigenfunctions corresponding to the non-Fock part of the spectrum will be constructed.
Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of…
We investigate the influence of superpositional wave function oscillations on the performance of Shor's quantum algorithm for factorization of integers. It is shown that the wave function oscillations can destroy the required quantum…
This paper is concerned with complex eigenvalues of truncated unitary quaternion matrices equipped with the Haar measure. The joint eigenvalue probability density function is obtained for truncations of any size. We also obtain the spectral…
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented.…
We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schr\"odinger picture. Generally in the most papers of the literature, the inverted harmonic oscillator is formally obtained from the harmonic…
Interference is one of the most fundamental features which characterizes quantum systems. Here we provide an exhaustive analysis of the interfere dynamics associated with wave-packet superpositions from both the standard quantum-mechanical…
This paper considers the effects of gravitational induced uncertainty on some well-known quantum optics issues. First we will show that gravitational effects at quantum level destroy the notion of harmonic oscillations. Then it will be…
We consider a thought experiment, in which a neutrino is produced by an electron on a nucleus in a crystal. The wave function of the oscillating neutrino is calculated assuming that the electron is described by a wave packet. If the…
The Fourier operator truncated on a finite symmetric interval is considered. The limiting behavior of its spectrum is discussed as the length of the interval tends to infinity.
Mesoscopic superpositions of distinguishable coherent states provide an analog to the Schr\"odinger's cat thought experiment. For mechanical oscillators these have primarily been realised using coherent wavepackets, for which the…
We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real and discrete, we show that the eigenfunctions do not form a…