Related papers: Comment on `Exact solution of the position-depende…
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…
In this paper, we search the dependence of some statistical quantities such as the free energy, the mean energy, the entropy, and the specific heat for the Schr\"odinger equation on the temperature, particularly the case of a non-central…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schr\"{o}dinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily…
Based on his extension of the classical argument of Einstein, Podolsky and Rosen, Schr\"odinger observed that, in certain quantum states associated with pairs of particles that can be far away from one another, the result of the measurement…
We consider the nonlinear Schrodinger equation under a partial quadratic confinement. We show that the global dispersion corresponding to the direction(s) with no potential is enough to prove global in time Strichartz estimates, from which…
We first present a consistent canonical formulation of the general (non-marginal) Oppenheimer-Snyder model. The switching between comoving and stationary observer is achieved by promoting coordinate transformations between dust proper time…
Using Schwinger Variational Principle we solve the problem of quantum harmonic oscillator with time dependent frequency. Here, we do not take the usual approach which implicitly assumes an adiabatic behavior for the frequency. Instead, we…
In this article, we study the scattering theory for the two dimensional defocusing quintic nonlinear Schr\"odinger equation(NLS) with partial harmonic oscillator which is given by \begin{align}\label{NLS-abstract} \begin{cases}\tag{PHNLS}…
Effective mass Schrodinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave…
In this paper we study some basic quantum confinement effects through investigation of a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation…
Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
We perform a theoretical and experimental study of a system of two ultracold atoms with tunable interaction in an elongated trapping potential. We show that the coupling of center-of-mass and relative motion due to an anharmonicity of the…
Wallstrom's criticism of existing formulations of stochastic mechanics is that they fail to derive the empirical predictions of orthodox quantum mechanics because they require an ad hoc quantization condition on the postulated velocity…
We obtain the exact energy spectra and corresponding wave functions of the radial Schr\"odinger equation (RSE) for any (n,l) state in the presence of a combination of psudoharmonic, Coulomb and linear confining potential terms using an…
We discuss a new completely integrable case of the time-dependent Schroedinger equation in $R^n$ with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator…
We present a unified, SI-consistent framework to constrain minimal SME coefficients $a_\mu$ and $b_\mu$ using magnetically confined two-dimensional electron systems under a uniform magnetic field. Working in the nonrelativistic…
In the statistical mechanics of quantum harmonic oscillators, the zero-point energy can either be included (Schr\"odinger oscillators) or omitted (Planck oscillators). For the usual results, the type of oscillator makes no difference but,…
In quantum mechanics courses, students often solve the Schr\"odinger equation for the harmonic oscillator with time-independent parameters. However, time-dependent quantum harmonic oscillators are relevant in modeling several problems as,…