Related papers: Quantum Binary Decision for Driven Harmonic Oscill…
The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…
Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation…
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…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{\Delta\mu_n\}_{n=0}^\infty$…
We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the…
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate…
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical…
Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum trajectory method. A new method is developed for calculating the resonance fluorescence spectra from numerical simulations. It…
This paper develops further the semi-classical theory of an harmonic oscillator acted on by a Gaussian white noise force discussed in (arXiv:1508.02379). Here I add to that theory the effects of Brownian damping (friction). Albeit…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding…
In this article, the optimal control problem for a harmonic oscillator with an inequality constraint is considered. The applied energy of the oscillator during a fixed final time period is used as the performance criterion. The analytical…
The Hamiltonian of the harmonic oscillator is usually defined as a differential operator, but an integral representation can be obtained by using the coherent state quantization. The finite frame quantization is a finite counterpart of the…
We consider the scenario of a fluctuating spacetime due to a deformed commutation relation with a fluctuating deformation parameter, or to a fluctuating metric tensor. By computing the resulting dynamics and averaging over these…
We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations [x_i,p_j]=i hbar[(1+ beta p^2) delta_{ij} + beta' p_i p_j]. These…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
The von Neumann interaction between a particle and an apparatus, both of arbitrary mass, has been considered in the measurement of the position of a simple harmonic oscillator acted on by an external force. When the measurement has finite…