Related papers: Ermakov equations in quantum mechanics
For the one-dimensional Helmholtz equation we write the corresponding time-dependent Helmholtz Hamiltonian in order to study it as an Ermakov problem and derive geometrical angles and phases in this context
A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential,…
We investigate the dynamics of interacting quantum harmonic oscillators coupled to thermal reservoirs under the influence of an external driving field. In a novel theoretical scheme, we first analyze the case of two interacting oscillators,…
Quantum entanglement has been actively sought for in optomechanical and electromechanical systems. The simplest such system is a mechanical oscillator interacting with a coherent beam, while the oscillator also suffers from thermal…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…
We consider the classical dynamics of two particles moving in harmonic potential wells and interacting with the same external environment (HE), consisting of N non-interacting chaotic systems. The parameters are set so that when either…
We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. A six parameter family of the square integrable oscillator wave functions, which seems cannot be obtained…
The destruction of quantum coherence by environmental influences is investigated taking the damped harmonic oscillator and the dissipative two-state system as prototypical examples. It is shown that the location of the coherent-incoherent…
In the quest for high-performance quantum thermal machines, looking for an optimal thermodynamic efficiency is only part of the issue. Indeed, at the level of quantum devices, fluctuations become extremely relevant and need to be taken into…
Or: ``How to generate an ensemble in a single event?'' Following recent work on entropy in strong interactions, I explain the concept of environment-induced quantum decoherence in elementary quantum mechanics. The classically chaotic…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
For the purpose of understanding the quantum behavior such as quantum decoherence, fluctuations, dissipation, entanglement and teleportation of a mesoscopic or macroscopic object interacting with a general environment, we derive here a set…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
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,…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
In many physical situations the behavior of a quantum system is affected by interaction with a larger environment. We develop, using the method of influence functional, how to deduce the density matrix of the quantum system incorporating…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…