Related papers: Harmonic oscillator in a one-dimensional box
The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two…
We revisit the quantum-mechanical two-dimensional harmonic oscillator with an electric field confined to a circular box of impenetrable walls. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with polynomial and…
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…
In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the…
We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the…
We study the size effect on the energy levels of the D-dimensional isotropic harmonic oscillator confined within a box of radius $r_c$ with impenetrable walls. Two different approaches are used to obtain the energy eigenvalues and…
We show that a system of four particles in a one-dimensional box with a two-particle harmonic interaction can by described by means of the symmetry point group $O_h$. Group theory proves useful for the discussion of both the small-box and…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
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.
We discuss the application of perturbation theory to a system of particles confined in a spherical box. A simple argument shows that the particles behave almost independently in sufficiently strong confinement. We choose the helium atom…
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…
We calculate the ground--state energy and other physical properties of the hydrogen atom inside a spherical box with an impenetrable wall. We apply the variational method and perturbation theory and compare both approximate results. We show…
We apply the Born--Oppenheimer approximation to a harmonic diatomic molecule with one electron. We compare the exact and approximate results not only for the internal degrees of freedom but also for the motion of the center of mass. We…
Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a…
In this paper we investigate the one-dimensional harmonic oscillator with a singular perturbation concentrated in one point. We describe all possible selfadjoint realizations and we show that for certain conditions on the perturbation…
We consider a quantum space with rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains tensors of noncommutativity constructed involving additional coordinates and momenta. In the rotationally…
In this note we consider high energy eigenfunctions of the harmonic oscillator in $\mathbb{R}^d$ and prove that any invariant measure on the energy surface can be written as a weak limit of eigenfunctions.
In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as…
The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent…
Within the approach of Supersymmetric Quantum Mechanics associated with the variational method a recipe to construct the superpotential of three dimensional confined potentials in general is proposed. To illustrate the construction, the…