Related papers: Harmonic oscillator in a one-dimensional box
We consider the Hamiltonian for a charged particle in a harmonic potential in the presence of a magnetic field. The most symmetric case depends on one parameter, the variation of which leads from a spectrum bounded from below to an…
Recently several authors studied the segregation of particles for a system composed of mono-dispersed inelastic spheres contained in a box divided by a wall in the middle. The system exhibited a symmetry breaking leading to an…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
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…
We study geometric quantization of the harmonic oscillator in terms of a singular real polarization given by fibres of the energy momentum map.
The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wave function for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete and it is given as a…
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…
We investigate a numerical method for studying resonances in quantum mechanics. We prove rigorously that this method yields accurate approximations to resonance energies and widths for shape resonances in the semiclassical limit.
The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its…
We study the closed Hamiltonian dynamics of a free particle moving on a ring, over one section of which it interacts linearly with a single harmonic oscillator. On the basis of numerical and analytical evidence, we conjecture that at small…
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,…
Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…
One-dimensional problem for quantum harmonic oscillator with "regular+random" frequency subjected to the external "regular+random" force is considered. Averaged transition probabilities are found.
We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum,…
We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail.…
We study the hydrogen atom confined to a spherical box with impenetrable walls but, unlike earlier pedagogical articles on the subject, we assume that the nucleus also moves. We obtain the ground-state energy approximately by means of…
Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillators in dimension one, two and three and we study its spectrum. In facts we give a detailed…