Related papers: Approximate stabilization of a quantum particle in…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…
I develop the solution to the problem of an electron confined in a composite quadratic well subject to a simple, external periodic force. The method of solution illustrates several of the basic techniques useful in formally solving the…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is neccessarily one with partial observations, and can generally be converted into a completely observed control…
This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schr\"odinger…
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle $2\theta_0$ emanating from the center of the sphere, with $0<\theta_0<\pi$. This non-central…
The role of edge states in phenomena like the quantum Hall effect is well known. In this paper we show how the choice of boundary conditions for a one-particle Schr\"odinger equation can give rise to states localized at the edge of the…
We consider the two dimensional Schr\"odinger equation with time dependent delta potential, which represents a model for the dynamics of a quantum particle subject to a point interaction whose strength varies in time. First, we prove global…
This paper studies the exponential stabilization on infinite dimensional system with impulse controls, where impulse instants appear periodically. The first main result shows that exponential stabilizability of the control system with a…
In modern fundamental theories there is consideration of higher dimensions, often in the context of what can be written as a Schr\"odinger equation. Thus, the energetics of bound states in different dimensions is of interest. By considering…
We describe an example of an exact, quantitative Jeopardy-type quantum mechanics problem. This problem type is based on the conditions in one-dimensional quantum systems that allow an energy eigenstate for the infinite square well to have…
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in…
We investigate optimal control strategies for state to state transitions in a model of a quantum dot molecule containing two active strongly interacting electrons. The Schrodinger equation is solved nonperturbatively in conjunction with…
In this paper, we study the almost sure well-posedness theory and orbital stability for the nonlinear Schr\"odinger equation with potential \begin{equation*} \left\{\begin{array}{l} i \partial_t u+\Delta u-V(x)u+|u|^{2}u=0,\ (x, t) \in…
A new family of 2-component vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented. They allow a consistent quantization of the classical phase space and observables for a particle in…
The general problem is studied on a simple example. A quantum particle in an infinite one-dimensional well potential is considered. Let the boundaries of well changes in a finite time $T$. The standard methods for calculating probability of…
In this article we prove semiglobal stabilization and exact controllability results for nonlinear plate equations with hinged boundary conditions and analytic nonlinearity. These results hold when the damping or control is localized in a…
We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…