Related papers: Wave-particle duality in the damped harmonic oscil…
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator…
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
Stunning progresses in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry and…
At present, there are many methods of quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
In this note, we apply canonical quantization to the self-dual particle system describing the motion of poles to a higher rank solution of the KP hierarchy, explicitly determining both the quantum Hamiltonian and the wave function. It is…
We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the…
Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit,…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for non-Markovian damped harmonic oscillator. In the general framework, the results demonstrate the possibility to use a closed system as a simulator…
A complete solution to the long standing problem of basing Schroedinger quantum theory on standard stochastic theory is given. The solution covers all "single" particle three-dimensional Schroedinger theory linear or nonlinear and with any…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…
Second quantization is an essential topic in senior undergraduate and postgraduate level Quantum Mechanics course. However, it seems that there is a lack of transparent and natural derivation of this formalism from the first-quantization…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
We derive the energy levels associated with the even-parity wave functions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical…
A finite number of harmonic oscillators coupled to infinitely many environment oscillators is fundamental to the problem of understanding quantum dissipation of a small system immersed in a large environment. Exact operator solution as a…
Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate…
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal…