Related papers: Perfect Quantum State Revivals: Designing Arbitrar…
We present a construction of semi-classical states for P\"oschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They…
One of the most important issues of quantum engineering is the construction of low-dimensional structures possessing desirable properties. For example, in different areas of possible applications of the structures containing quantum wells…
A general approach for constructing multidimensional quasi-exactly solvable (QES) potentials with explicitly known eigenfunctions for two energy levels is proposed. Examples of new QES potentials are presented.
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…
There are various types of infinite potential well problems occurring in elementary quantum mechanics formalism. The infinite square well (one dimensional), cubical box and, spherical well are quite common in textbooks. In this paper, we…
We calculate the quantum revival time for a wave-packet initially well localized in a one-dimensional potential in the presence of an external periodic modulating field. The dependence of the revival time on various parameters of the driven…
The quantum mechanical bound states of the $-{\alpha}/x^2$ potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the…
We propose a new method for constructing the quasi-exactly solvable (QES) potentials with two known eigenstates using supersymmetric quantum mechanics. General expression for QES potentials with explicitly known energy levels and wave…
An infinite sequence of potential well functions is considered. A numerical method is used for the Schr$\ddot{\text{o}}$dinger equation to obtain the energy eigenvalue spectra for a number of these potential well functions. The results for…
Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…
Supersymmetric method of the constructing well-like quasi exactly solvable (QES) potentials with three known eigenstates has been extended to the case of periodic potentials. The explicit examples are presented. New QES potential with two…
An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…
It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the…
The Kronig-Penney model describes what happens to electron states when a confining potential is repeated indefinitely. This model uses a square well potential; the energies and eigenstates can be obtained analytically for a the single well,…
The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites.…
The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially…
Most quantum tomographic methods can only be used for one-dimensional problems. We show how to infer the quantum state of a non-relativistic N-dimensional harmonic oscillator system by simple inverse Radon transforms. The procedure is…
We consider a non relativistic charged particle in a 1-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It is represented by a complex…
Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…